light travelling along a normal is dash refracted

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Snell's Law

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Andrew Ellinor
Rishik Jain
Someguy Noname

Snell's law , also known as the law of refraction , is a law stating the relationship between the angles of incidence and refraction, when referring to light passing from one medium to another medium such as air to water, glass to air, etc.

Explanation

Refraction through a glass slab, lateral displacement and it's calculation, normal shift, total internal reflection, effects and applications of total internal reflection, snell's law - problem solving.

Snell's Law states that the ratio of sine of angle of incidence and sine of angle of refraction is always constant for a given pair of media. \[\dfrac{\sin i}{\sin r}=\text{constant}=n=\text{refractive index}\]

Let us consider that light enters from medium 1 to medium 2,

\[\therefore \dfrac{\sin i}{\sin r}=n_{21}=\dfrac{n_2}{n_1}=\dfrac{\color{blue}{v_1}}{\color{blue}{v_2}}=\dfrac{\color{blue}{\lambda_1}}{\color{blue}{\lambda_2}}\]

Here, $v_n$ is the velocity of light in respective medium and $\lambda_n$ is the wavelength of light in respective medium. You may be wondering how we obtained the expression in blue color, well if we define it in an easy way, the basic cause of refraction is due to the change in velocity of light by entering a medium of different refractive index. So, if a medium has less refractive index, then the velocity of light in that medium would be more but if a medium has more refractive index then the velocity of light in that medium would be comparatively less.

\[\therefore v \propto \dfrac{1}{n} \Rightarrow \dfrac{v_1}{v_2}=\dfrac{n_2}{n_1}=n_{21}\]

Question: A ray of light travelling in air is incident on the plane surface of a transparent medium. The angle of incidence is found to be $45^{\circ}$ and the angle of refraction is $30^{\circ}$. Find the refractive index of the medium. Solution: We know that $\hat i=45^{\circ}$ and $\hat r=30^{\circ}$ Therefore refractive index, \[\begin{align} n=\dfrac{\sin i}{\sin r} &= \dfrac{\sin 45^{\circ}}{\sin 30^{\circ}}\\ &= \dfrac{1/\sqrt{2}}{1/2}= \sqrt{2} \end{align}\]

A ray of light is incident on a surface at an angle of $60^\circ$, refracts at an angle of $45^\circ$. Find it's refractive index.

Round your answer to 3 decimal places.

Absolute Refractive Index:

When we compare the speed of light in a medium to that of the speed of the light in vacuum , then we would be dealing with something called absolute refractive index. We generally refer to the absolute refractive index of a medium when we say that a certain object's refractive index is $x$.

The expression for the absolute refractive index of a medium would thus be: \[\text{absolute refractive index}=\dfrac{\text{speed of light in vacuum}}{\text{speed of light in the given medium}} = \dfrac{c}{v}\]

Note: As the speed of light is at its maximum in vacuum, the absolute refractive index always greater than $1$. Also note that the refractive index is a relative quantity and thus it had no units.

Question: The absolute refractive index of a glass window is $1.5$. What is the speed of light when it is traveling through the glass window? Assume that the speed of light in vacuum $=3\times 10^8m/s$. Solution: According to the question, we have: \[\dfrac{\text{speed of light in vacuum}}{\text{speed of light in the given medium}}=1.5\\ \implies \dfrac{3\times 10^8}{\text{speed of light in the given medium}}=1.5\\ \implies \text{speed of light in the given medium}=\dfrac{3\times 10^8}{1.5}=\boxed{2\times 10^8 m/s}\]

Question: The absolute refractive index of diamond is $2.42$. What is the speed of light in diamond? (Take speed of light in vacuum= $3 \times 10^8 m/s$ Solution: Absolute refractive index of diamond is \[=\dfrac{\text{speed of light in vacuum}}{\text{speed of light in diamond}}\quad\therefore\dfrac{c}{v}=2.42\\ \implies v=\dfrac{c}{2.42} \implies v=\dfrac{3 \times 10^8}{2.42} \\\boxed{v=1.24 \times 10^8 m/s}\]

Refraction of a ray of light in a glass slab

In this case, we will try to prove $\angle i_1=\angle r_2$ or the incident ray is parallel to the emergent ray,

Applying Snell's Law when the light is incident on the glass slab's surface,

\[\dfrac{\sin i_1}{\sin r_1}=n=\text{refractive index of glass}\]

Now, applying Snell's Law when the light ray is leaving the glass slab through another surface,

\[\dfrac{\sin i_2}{\sin r_2}=\dfrac{1}{n}\Rightarrow \dfrac{\sin r_2}{\sin i_2}=n=\text{refractive index of glass} \\ \therefore \dfrac{\sin i_1}{\sin r_1}=\dfrac{\sin r_2}{\sin i_2}\]

Now, $\angle r_1=\angle i_2$ as they are alternate angles, thus, $\sin r_1=\sin i_2$,

\[\therefore \sin i_1=\sin r_2\Rightarrow \angle i_1=\angle r_2 \]

So, the incident ray is parallel to the emergent ray but it is laterally displaced from it.

Question: A ray of light travelling in air falls on the surface of a transparent glass slab. The ray makes and angle of $45^{\circ}$ with the normal to the surface. Find the angle made by the refracted ray with the normal within the slab. Given that refractive index of the glass slab is $\sqrt{2}$. Solution: We know that $ n=\dfrac{\sin i}{\sin r} = \dfrac{\sin 45^{\circ}}{\sin r}$, here the refractive index is $\sqrt{2}$. \[\begin{align} \dfrac{\sin 45^{\circ}}{\sin r}&=\sqrt{2}\\ \implies\sin r &= \dfrac{1}{\sqrt{2}}\times \sin 45^{\circ}\\ =\dfrac{1}{\sqrt{2}}\times \dfrac{1}{\sqrt{2}} &=\dfrac{1}{2} \end{align}\] Thus, as $\sin r$ = $\dfrac{1}{2}$, the angle of refraction would be $r=\sin^{-1}\left(\dfrac 12\right)=30^\circ$.

As discussed earlier, the emergent ray is parallel to the incident ray but appears slightly shifted, and this shift in the position of the emergent ray as compared to the incident ray is called Lateral displacement .

Lateral Displacement The perpendicular distance between the incident ray and the emergent ray is defined as lateral shift. This shift depends upon the angle of incidence, the angle of refraction and the thickness of the medium. It is given by the following expression: \[S_{\text{Lateral}}=\dfrac{t}{\cos r}\sin{(i-r)}\]

We shall now try to derive the above stated formula for a Glass slab. In the figure given below, $AB$ is the incident ray, $BC$ is the refracted ray and $CD$ is the emergent ray. The ray is striking the slab at an angle of $i_1$ and it is emerging from the slab at an angle of $r_2$.

Refraction of a ray of light in a glass slab with it's corresponding angles

In $\triangle BCK$,

\[\sin (i_1-r_1)=\dfrac{CK}{BC} \Rightarrow CK=BC \sin (i_1-r_1)\]

In $\triangle BCN'$,

\[\cos r_1=\dfrac{BN'}{BC}=\dfrac{t}{BC} \Rightarrow BC=\dfrac{t}{\cos r_1}\]

Here, $t$ is the thickness of slab.

Substituting the value of $BC$ in the first equation,

\[S_L=\text{Lateral Displacement }(CK)=t\dfrac{\sin(i_1-r_1)}{\cos r_1}\]

Question: The thickness of a glass slab is $0.25m$, it has a refractive index of $1.5$. A ray of light is incident on the surface of the slab at an angle of $60^\circ$. Find the lateral displacement of the light ray when it emerges from the other side of the mirror. You may assume that the speed of light is $3\times 10^8 m/s$. Solution: From the previous topics, we know: \[\text{refractive index}=\dfrac{\sin i}{\sin r}=1.5\text{ (in this case)}\\\sin r=\dfrac{1.5}{\sin 60}\approx 0.57735\\\implies r = \sin^{-1}(0.57735)\approx 35.25^\circ\] Now, applying the values in the formula for lateral displacement we get: \[S_L=\dfrac{0.25}{\cos(35.25)}\times\sin(60-35.25)\approx 0.1281 m =\boxed{12.81cm}\]

Many a time you might have seen the floor of the swimming pool raised/ the letters appearing to be raised under a glass slab, ever wondered why this happens? If you observe clearly, you'll find that refraction explains it. Let's see the definition.

The vertical distance by which an object appears to be shifted when an object placed in one medium is observed from another medium of different refractive indices, is called Normal shift. It is given by the formula: \[S_{\text{Normal}}=t\left(1-\dfrac{1}{_{\text r}n_{\text d}}\right)\quad\text{where}\quad _{\text r}n_{\text d}=\mu=\dfrac{\text{real depth}}{\text{apparent depth}}\]

The thickness of a glass slab is $0.2m$, and it is placed over a flat book, the refractive index of the glass slab is $1.5$. A student looks through it and finds that the normal shift is $x$, find $x$. Solution: We know that: \[\begin{align} S_N&=t\left(1-\dfrac{1}{\mu}\right)\\ &=0.2\left(1-\dfrac{1}{1.5}\right)\\ &=0.2\times \dfrac 13= 0.066m \end{align}\]

When light travels from a denser to rarer medium with an angle greater than the critical angle, the ray of light does not deviate in its path or does not refract, but it undergoes a reflection known as total internal reflection. The angle beyond which light in a given medium undergoes total internal reflection is called the critical angle .

The critical angle differs from medium to medium. If the refractive index of a given medium is $\mu$, then it's critical angle is given by the formula: [1]

\[\mu =\dfrac { 1 }{ \sin{ \theta }_{ c } }\quad\\\theta_c=\sin^{-1}\left(\dfrac 1\mu\right)\]

This is very useful as it is used in fiber glasses where total internal reflection helps in fast movement of wavelengths.

Sparkle of the diamond Whenever your mom wears it you notice it, yes the sparkling beauty of the diamond never misses our eye. But have you ever wondered why the diamond sparkles? Well it is due to the phenomenon we've been discussing now, total internal reflection . Sparking beauty of the hope diamond [2]

Mirage Formation This very old illusion ,which had fooled many people, is due to the magic of Total Internal relfection! Mirage is an optical illusion caused by refraction and total internal reflection. We know that the temperature of air varies with height, and also refractive index depends on the temperature of the medium. Mirage Formation on a road [3] During hot summers, the Surface of the Earth gets hotter, and the layers of air with decreasing temperature are formed. But the hot air has a refractive index lower than the cold air, that is hot air is optically rarer than cold air, and we know if a ray of light passes through a rarer medium from a denser medium, then the light rays bend away from the normal. So, at some points the light rays get totally reflected internally and reach the eyes of an observer, creating the reflection of an object on the surface of the Earth.

Looming Very similar to mirage formation,thus phenomenon makes the objects appear to be levitating in the sky. This is mostly seen in the polar regions (as opposed to mirages, which are generally frowned in hot deserts). In these places the surface of the Earth is very cold and as we go up, layers of air with increasing temperatures are formed. As a result, the layers of atmosphere near the Earth have a higher refractive index than the layers above them, this layer is called as an inversion layer . The objects appear to be floating due to the phenomemnon of looming [4] When the light from any object (normally ships) reaches an observer, it undergoes a series of refractions which makes the light rays bend away from the normal, and at a point, they reach a stage where the angle incidence is greater than the critical angle and thus the rays undergo total internal reflection and reach the eye of an observer and creates and optical illusion that the object is really floating in the sky!

Fibre Optics Optical fibres are the devices used to transfer light signals over large distances with negligible loss of energy . It is a revolutionary idea in terms of communication. But it's working is based on this simple phenomenon of total internal reflection. If you take a close look at an optical fibre you will observe that it consists of a thin transparent material, this is know as the core . This core is coated with something known as cladding and has a higher refractive index than the surrounding medium [5] , it prevents the absorption of light by any means. The internal structure and the transfer of light signal in a single optical fibre [6] When the light rays enter the acceptance cone, some rays which are incident at an angle greater than the critical angle gets reflected internally and then it undergoes a series of Total Internal reflections until it reaches the other end of the firbe. But we should note that not all of the rays get reflected internally because they may not have struck the surface at the required angle (as seen in the figure above).

The critical angle is the angle of incidence above which total internal reflection occurs. If the speed of light is $1.5 \times 10^8\text{ m/s}$ in a particular medium, then what is the critical angle of the light passing through this medium into the air?

The speed of light in the air is $3.0 \times 10^8\text{ m/s}.$

Optical fibers are devices used for guiding light in many applications, most notably for fast communication. A fiber consists of a glass cylinder surrounded by a wall covered in a special coating.

The fibers work on a principle called total internal reflection : light enters the fiber at an angle such that it does not get transmitted through the wall of the fiber when it hits the inside of the wall. Therefore, the refraction index of the glass part of the fiber has to be higher than that of its coating.

What is the maximum entering angle in degrees a light ray can pass from the air to the glass fiber for the total internal reflection to occur?

Details and Assumptions:

Measure the entering angle from the axis of the fiber.
Use the following refraction indexes: $n_{\text{air}} = 1.00$, $n_{\text{glass}} = 1.50,$ and $n_{\text{coating}} = 1.46$.

[1] Total Internal reflection, rp-encyclopedia.com . Retrieved 16:45, March 15, 2016, from https://www.rpphotonics.com/total internal reflection.html .

[2] Image from https://en.m.wikipedia.org/wiki/Diamond#/media/File%3AThe Hope Diamond - SIA.jpg under the creative Commons license for reuse and modification.

[3] Image credit http://epod.usra.edu/blog/2010/03/highway-mirage.html : Universities Space Research Association

[4] Image from https://en.m.wikipedia.org/wiki/File:Illustration of looming refration phenomenon.jpg under the creative Commons license for reuse and modification.

[5] Optical Fibres, rp-encyclopedia.com . Retrieved 08:56, March 17, 2016, from https://www.rpphotonics.com/fibers.html .

[6] Image credit http://www.pacificcable.com/Fiber-Optic-Tutorial.html .

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$light travelling along a normal is dash refracted$

Refraction Towards the Normal

The diagram shows an incident ray of white light approaching the boundary between air and glass.

As the ray crosses the boundary and encounters the glass it bends towards the normal (the dotted green line).
The incident ray of light is refracted towards the normal because the ray travels from air, the faster, less optically dense medium with a lower refractive index into the glass, a slower, more optically dense medium with the higher refractive index .

Description

Try some quick questions and answers to get started.

About the diagram

Have you already checked out An Introduction to Reflection, Refraction and Dispersion ?

It is the opening page of our Reflection , Refraction and Dispersion Series and contains mass es of useful information. This is the table of contents:

Introducing reflection
Types of reflection
Introducing refraction

Calculating the angle of refraction

Introducing chromatic dispersion
Introducing refraction and wavelength

Overview of this page

This page provides an introduction to refraction .
It looks at the path of white light rather than at the paths of the different wave lengths that white light contains.
Related topics including reflection and dispersion are covered on other pages of this series.
Introductions to the terms refractive index and the law of refraction (sometimes called Snell’s law) also appear on later pages in the series.

An overview of refraction

Refraction refers to the way that light ( electromagnetic radiation ) changes direction and speed as it travels from one transparent medium into another.
Refraction takes place as light travels across the boundary between different transparent media and is a result of their different optical properties.
When light is refracted its path bends and so changes direction.
The effect of refraction on the path of a ray of light is measured by the difference between the angle of incidence and the angle of reflection .
As light travels across the interface between different media (such as between air and glass) it changes speed.
Depending on the media through which light is refracted, its speed can increase or decrease.
This diagram shows an incident ray of white light approaching the boundary between air and glass.
The diagram shows that the angle of incidence and the angle of refraction of the ray of light are different as a result of refraction.
As the ray crosses the boundary from the air and encounters the glass, it bends towards the normal (the dotted green line) because glass is an optically denser medium (with a higher refractive index than air) that slows it down.
Imagine running into the wind. It’s always harder to run in water because it is a physically denser medium than air. The physical density of a substance is similar to the optical density of a transparent medium.
When light crosses the boundary between two different transparent media it undergoes refraction.
The effect of refraction is that light changes speed along with its direction of travel.
As the speed of light changes so does its wavelength but the frequency and so the colour an observer sees remains the same.
The result of the change in direction is that rays either bend towards or away from the normal.
The normal is an imaginary line drawn on a ray diagram at right angles (perpendicular) to the boundary between two media.
The change between the angle of incidence and the angle of refraction of a ray of light is always measured between the ray and the normal.
Whether light bends towards or away from the normal depends on the difference in optical density of the new medium it encounters.
An incident ray of light is refracted towards the normal and slows down when it travels from air into glass. Compared with air, glass is a slower, more optically dense medium (with the higher refractive index).
An incident ray of light is refracted away from the normal and speeds up when it travels from glass into air. Compared with glass, air is a faster, less optically dense medium (with a lower refractive index).
The direction in which a ray bends, and the precise angle, can be calculated if the type and refractive indices of both media are known.
The effect of refraction can be calculated using a neat little equation called the law of refraction (also known as Snell’s law).
If three of the variables are known, the law of refraction can be used to calculate the fourth.
Tables of refractive indices are available for common material s so that the change in direction of a ray can be calculated.
Tables of refractive indices for common materials often provide both the refractive index for white light as well as indices for specific wavelengths.

For an explanation of the refractive index ( index of refraction ) of a medium see: Refractive Index Explained.

For an explanation of how to use the refractive index of a medium see: How to Use the Refractive Index of a Medium.

For an explanation of the Law of Refraction see: Snell’s Law of Refraction Explained .

Incident light

Incident light refers to incoming light that is travelling towards an object or medium.

White light

White light is the name given to visible light that contains all wavelengths of the visible spectrum at equal intensities.
The sun emits white light because sunlight contains equal amounts of all of the wavelengths of the visible spectrum .
As light travels through a vacuum or a medium it is described as white light if it contains all the wavelengths of visible light .
As light travels through a vacuum or the air it is invisible to our eyes.
White light is what an observer sees when all the colours that make up the visible spectrum strike a white or neutral coloured surface.

Visible spectrum

The visible spectrum is the range of wavelengths of the electromagnetic spectrum that correspond with all the different colours we see in the world.
Human beings don’t see wavelengths of visible light, but they do see the spectral colours that correspond with each wavelength and colours produced when different wavelengths are combined.
The visible spectrum includes all the spectral colours between red and violet and each is produced by a single wavelength.

Angle of incidence

The angle of incidence measures the angle at which incoming light strikes a surface.
The angle of incidence is measured between a ray of incoming light and an imaginary line called the normal.

Angle of refraction

The angle of refraction measures the angle to which light bends as it passes across the boundary between different media.
The angle of refraction is measured between a ray of light and an imaginary line called the normal.

Optical density

Optical density is a measurement of the degree to which a medium slows the transmission of light.
The more optically dense a material, the slower light travels.
The less optically dense a material, the faster light travels.
In geometry, the normal is a line that intersects another line.
In optics , the normal is an imaginary line drawn on a ray diagram at right angles (perpendicular) to the boundary between two media.
The normal is often used to measure angles against.

Some key terms

In physics and optics , a wave diagram uses a set of drawing conventions and labels to describe the attributes of light wave s including wavelength , frequency , amplitude and direction of travel.

A wave diagram illustrates what happens to a wave as it encounters different media or object s.
The aim of a wave diagram is to demonstrate optical phenomena such as reflection and refraction .

The frequency of electromagnetic radiation ( light ) refers to the number of wave-cycle s of an electromagnetic wave that pass a given point in a given amount of time.

Light travels through different media such as air, glass or water at different speeds. A fast medium is one through which it passes through more quickly than others.

Light travels through a vacuum at 299,792 kilometres per second.
Light travels through other media at lower speeds.
In some cases, it travels at a speed which is near the speed of light (the speed at which light travels through a vacuum) and in other cases, it travels much more slowly.
It is useful to know whether a medium is fast or slow to predict what will happen when light crosses the boundary between one medium and another.
If light crosses the boundary from a medium in which it travels fast into a material in which it travels more slowly, then it will bend towards the normal .
If light crosses the boundary from a medium in which it travels slowly into a material in which it travels more quickly, then the light ray will bend away from the normal .
In optics , the normal is a line drawn in a ray diagram perpendicular to, so at a right angle to (90 0 ), to the boundary between two media.

The refractive index of a medium is the amount by which the speed (and wavelength ) of electromagnetic radiation ( light ) is reduced compared with the speed of light in a vacuum.

Refractive index (or, index of refraction ) is a measure of how much slower light travels through any given medium than through a vacuum.
The concept of refractive index applies to the full electromagnetic spectrum , from gamma- ray s to radio wave s.
The refractive index of a medium is a numerical value and is represented by the symbol n.
Because it is a ratio of the speed of light in a vacuum to the speed of light in a medium there is no unit for refractive index.
If the speed of light in a vacuum = 1. Then the ratio is 1:1.
The refractive index of water is 1.333, meaning that light travels 1.333 times slower in water than in a vacuum. The ratio is therefore 1:1.333.
As light undergoes refraction its wavelength changes as its speed changes.
As light undergoes refraction its frequency remains the same.
The energy transported by light is not affected by refraction or the refractive index of a medium.
The colour of refracted light perceived by a human observer does not change during refraction because the frequency of light and the amount of energy transported remain the same.

In physics and optics , a medium refers to any material (plural: media) through which light or other electromagnetic waves can travel. It’s essentially a substance that acts as a carrier for these wave s.

Light is a form of electromagnetic radiation , which travels in the form of waves. These waves consist of oscillating electric and magnetic fields .
The properties of the medium, such as its density and composition, influence how light propagate s through it.
Different mediums can affect the speed, direction, and behaviour of light wave s. For instance, light travels slower in water compared to a vacuum.
Transparent: Materials like air, glass, and water allow most light to pass through, with minimal absorption or scattering . These are good examples of mediums for light propagation .
Translucent: Some materials, like frosted glass or thin paper, partially transmit light. They allow some light to pass through while diffusing or scattering the rest.
Opaque: Materials like wood or metal block light completely. They don’t allow any light to travel through them.
Refraction : Bending of light as it travels from one medium to another with different densities.
Reflection : Bouncing back of light when it encounters a boundary between mediums.
Absorption : Light being captured and converted into other forms of energy (like heat) by the medium.

Related diagrams

http://wikidiff.com/vacuum/medium
https://en.wikipedia.org/wiki/Transmission_medium
In physics and optics, a medium refers to any material through which light or other electromagnetic wave s can travel. It’s essentially a substance that acts as a carrier for these waves.
Light is a form of electromagnetic radiation , which travels in the form of waves. These waves consist of oscillating electric and magnetic field s.

Wavelength is a measurement from any point on the path of a wave to the same point on its next oscillation . The measurement is made parallel to the centre-line of the wave.

The wavelength of an electromagnetic wave is measured in metres.
Each type of electromagnetic radiation , such as radio waves, visible light and gamma waves, forms a band of wavelengths on the electromagnetic spectrum .
The visible part of the electromagnetic spectrum is composed of the range of wavelengths that correspond with all the different colour s we see in the world.
Human beings don’t see wavelengths of visible light , but they do see the spectral colour s that correspond with each wavelength and the other colours produced when different wavelengths are combined.
The wavelength of visible light is measured in nanometre s. There are 1,000,000,000 nanometre s to a metre.

As light crosses the boundary between two transparent media, the law of refraction (Snell’s law) states the relationship between the angle of incidence and angle of refraction of the light with reference to the refractive indices of both media as follows:

When electromagnetic radiation (light) of a specific frequency crosses the interface of any given pair of media, the ratio of the sine s of the angles of incidence and the sine s of the angles of refraction is a constant in every case.

Snell’s law deals with the fact that for an incident ray approaching the boundary of two media, the sine of the angle of incidence multiplied by the index of refraction of the first medium is equal to the sine of the angle of refraction multiplied by the index of refraction of the second medium.
Snell’s law deals with the fact that the sine of the angle of incidence to the sine of the angle of refraction is constant when a light ray passes across the boundary from one medium to another.
Snell’s law can be used to calculate the angle of incidence or refraction associated with the use of lenses, prism s and other everyday material s.
The angles of incidence and refraction are measured between the direction of a ray of light and the normal – where the normal is an imaginary line drawn on a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.
The wavelength of the incident light is accounted for.
The refractive indices used are selected for the pair of media concerned.
The speed of light is expressed in metres per second (m/s).

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Light, which is travelling along a normal, is ............ refracted Partially Completely Not All

The light travelling along normal don't get refracted and passes undeviated. answer-(c)..

Fill in the following blanks with suitable words : (a) Light travelling along a normal is ___ refracted. (b) Light bends when it passes from water into air. We say that it is ___ .

Light travelling from a denser medium. to a rarer medium alone a normal to the boundary : (a) is refracted towards the normal (b) is refracted away from the normal (c) goes along the boundary (d) is not refracted

$light travelling along a normal is dash refracted$

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StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

$light travelling along a normal is dash refracted$

StatPearls [Internet].

Refraction of light.

Kirandeep Kaur ; Bharat Gurnani .

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Last Update: July 17, 2023 .

Definition/Introduction

The refraction of light is the bending of light rays as they pass from one medium to another, thereby changing the path of the rays. Refraction occurs due to a change in the speed of the light ray or wave. [1] The speed of light is greatest in a vacuum. When the light rays travel from a rarer to a denser medium, they bend towards the normal. If the light rays travel from a denser to a rarer medium, they bend away from the normal. [2] The greater the density of the media, the higher the refractive index. Snell’s law, or the law of refraction, quantitatively defines the amount of bending of waves dependent on the refractive index of the two media.

The refraction of light has applications in ophthalmic physics. Light refraction in nature is what creates rainbows, optical illusions, the formation of mirages, and the twinkling of stars. [2] The refraction phenomenon also occurs with sound, water, and other waves. Light rays can be bent by spectacle lenses, magnifying glasses, prisms, and water droplets. Without the refraction of light, our eyes may not be able to focus clearly. [3]

Issues of Concern

Refraction Terminology

The normal line, or normal (N), is a line drawn perpendicular to the boundary at the point of incidence. A dotted line usually indicates the normal in a ray diagram. The point of incidence is where the incident ray strikes the boundary between the two media. [4]

The incident ray is the light ray approaching and striking the refracting surface, which occurs at the boundary of two media. After the incident ray strikes the refracting surface, it bends and is now a refracted ray. The angle of incidence (Θ i ) is defined as the angle between the incident ray and the normal. The angle of refraction (Θ r ) is the angle between the normal and the refracted ray. [5] The incident and refracted rays are on the opposite sides of normal, and all three vectors align in one plane.

Law of Refraction

The relationship between the angles of incidence and refraction and the indices of refraction of the two media is known as the Law of Refraction or Snell's law. [6] This law applies to the refraction of light in any situation, regardless of what the two media are. The index of refraction of each media (n) is a constant. The index of refraction for a vacuum is 1. The index of refraction for air is so close to 1 that the difference is immeasurable to us.

The incident ray traveling through the incident medium, with a refractive index of n i , strikes the refractive surface of the second medium, with a refractive index of n r , and becomes the refracted ray. Mathematically, this is:

n i ⋅ sin(Θ i ) = n r ⋅ sin(Θ r )

The critical angle is defined as the angle of incidence that creates an angle of refraction of 90 degrees. It is the largest angle of incidence for which refraction can still occur. Light will undergo total internal reflection for any angle of incidence greater than the critical angle. Total internal reflection will only occur if the incident light ray is in an optically denser medium and approaching an optically rarer medium, and the angle of incidence for the light ray is greater than the critical angle. Optical density is a measure of the tendency of a material to slow down any light traveling through it. [7] [8]

Types of Refraction

Refraction Through a Plane Media

When refraction occurs through a plane media, as when light travels through the air across an incident surface like a glass plate, some of the light is reflected off from the surface, and some is transmitted through the surface. The reflected, or emergent, rays (E) are deflected away from the normal line of the incident surface. The incident rays (I) will deflect toward the normal line of the incident surface. This deflection of incident light rays toward the normal in the denser medium (the glass) is responsible for objects appearing nearer than they actually are. Alternatively, when incident rays travel from an optically denser medium to an optically rarer medium, objects will appear further away than they actually are. [9]

When light rays travel from optically rarer to optically denser media, the incident light rays (I) bend towards the normal, and the angle of refraction (Θ r ) is less than that of the angle of incidence (Θ i ). [10] When the incident light rays (I) travel from an optically denser to an optically rarer medium, the light rays bend away from the normal, and the angle of refraction (Θ r ) is greater than the angle of incidence (Θ i ). [11]

Refraction Through a Prism

A triangular prism is a transparent refracting medium bound by five planar surfaces, each inclined at an angle. The refracting or apical angle is the angle of a prism formed by two adjacent surfaces. The greater the angle between the two surfaces, the more the prismatic effect.

The axis of the prism is a line bisecting the apical angle, and the base of the prism is the surface opposite the apical angle. The orientation of a prism is indicated by the position of the base, whether base-in, base-out, base-up, or base-down. [12]

Light rays passing through a prism follow the fundamental law of refraction at each incident surface, and the incident ray will deviate toward the base of the prism.

The refractive index of a glass prism is defined as:

η = {Sin[(A + δ)/2]} ÷ sin(A/2), where
η = refractive index of a glass prism
A = angle of the prism (angle between the two sides of the reflecting faces of the prism)
δ = angle of deviation [13]

The angle of deviation is the change in the direction of the incident light ray as it passes through the prism. Mathematically, the angle of deviation is the angle between the incident ray as it passes through the first face of the prism and the refracted emergent ray that emerges from the second face of the prism (Image. Refraction of Light Through a Glass Prism). The angle of deviation is governed by the following:

μ = material of the prism
A = angle of the prism
Θ i = angle of incidence of the incident ray
λ = wavelength of light of the incident ray

The angle of minimum deviation occurs when refraction is symmetrical — when the angle of incidence equals the angle of emergence. The image formed by a prism is upright, virtual, and displaced toward the apex. The power of the prism is denoted in prism diopters and is dictated by the apical prism angle. A 1-diopter prism will displace an object 1 cm at a distance of 1 m. One prism diopter of displacement is central or 0.57 degrees of an arc. When incorporating prism optics into an ophthalmic lens, the following rules apply:

The amount of correction should be split between both eyes
Base-out prisms should be prescribed in esodeviations
Base-in prisms should be prescribed in exodeviations

ATD (apex towards the deviation) is an acronym to remember to prescribe prisms for correcting esodeviations. [14]

Refraction at a Curved Surface

Refraction at a curved surface is essential for ophthalmology because the cornea is a curved convex surface. When rays of light strike a spherical surface separating two transparent media with different refraction indices, the light rays will be refracted in the same plane per the law of refraction. The amount of refraction will depend on the angle of incidence and dioptric power of the spherical surface. [15]

The power of a spherical refracting surface in diopters is equal to the difference in refractive indices of the two media divided by the radius of the curvature. Mathematically, this is:

D = (n'-n)/r, where
D = power in diopters
r = radius of curvature of the refracting surface
n' = the refraction index of the right side of the surface, assuming a ray moving from left to right
n = the refractive index of the surface. The sign convention of r is positive to the right of the surface and negative towards the left of the surface. [16]

During retinoscopy, a patient focusing on a near object instead of a far distance might give a pseudo-myopic reading. Focusing on a near object for a longer period results in an accommodative spasm. Refraction may not yield the correct result in these patients. [17]

Clinical Significance

The principles of total internal reflection and prism refraction are used in many clinical instruments such as applanation tonometers, gonioscopes, keratometers, slit-lamp microscopes, and fiberoptic cables.

Fiber Optical Devices

Optical fibers are thin, flexible glass rods that carry light from one end to the other using total internal reflection. A bundle of optical fibers is called a light pipe. An optical fiber consists of a central core graded smoothly into an outer cladding layer with a lower refraction index. This fiber is usually coated in a protective sheath. Only the internally reflected rays are propagated along the fiber. Such fibers form the basis of endoscopes used extensively in gastroenterology, urology, general surgery, and gynecology. [18]

Prisms can be used for diagnostic or therapeutic purposes.

Prisms used for diagnostic purposes include unmounted loose prisms, trial lens-mounted prisms, and vertical or horizontal prism bars. Prisms may be used to predict diplopia in children undergoing surgical strabismus correction or to diagnose malingering. The prism cover test and Krimsky test contribute to the objective measurement of the angle of deviation, which can also be measured subjectively using a Moddox rod. The four-prism diopter test can diagnose microtopia, and prisms may also be used to measure fusional reserve.

Prisms also have therapeutic applications, relieving diplopia in patients with decompensated phorias, low hypermetropia, and paralytic strabismus with diplopia in the primary position. In patients with convergence insufficiency, prisms may be used to build up fusional reserve; it is recommended to utilize a base-out prism only during the exercise period.

Prisms for temporary wear include clip-on spectacle prisms and Fresnel prisms. Fresnel prisms are tiny prisms manufactured from plastic sheets that can be adhered to spectacles. However, prisms for permanent wear are inserted into the spectacles by decentering the prescribed spherical lenses. When a spherical correction is not required, prisms can be mounted on the spectacle frame.

Nursing, Allied Health, and Interprofessional Team Interventions

The optometrist, ophthalmologist, optometry technicians, and clinical support staff work in concert to enhance outcomes for patients with refractive error. Open and effective communication among team members ensures that everyone clearly understands the patient's condition and treatment plan. A holistic approach to patient assessment, considering the physical, emotional, social, and environmental factors that can influence vision, promotes patient adherence to treatment plans.

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Refraction of light through a glass prism. Contributed by Kirandeep Kaur, MD

Disclosure: Kirandeep Kaur declares no relevant financial relationships with ineligible companies.

Disclosure: Bharat Gurnani declares no relevant financial relationships with ineligible companies.

This book is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ), which permits others to distribute the work, provided that the article is not altered or used commercially. You are not required to obtain permission to distribute this article, provided that you credit the author and journal.

Cite this Page Kaur K, Gurnani B. Refraction of Light. [Updated 2023 Jul 17]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

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24.2: Reflection, Refraction, and Dispersion

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learning objectives

Formulate the relationship between the angle of reflection and the angle of incidence

Whenever you look into a mirror or squint at sunlight glinting off a lake, you are seeing a reflection. When you look at the text in a book, you are actually seeing the light that is reflected from it. Large telescopes use reflections to form images of stars and other astronomical objects. In fact, the only way we can see an object that does not itself emit light is if that object reflects light.

The law of reflection is illustrated in, which also shows how the angles are measured relative to the perpendicular to the surface at the point where the light ray strikes. The law of reflection is very simple: The angle of reflection equals the angle of incidence. When we see our reflection in a mirror, it appears that our image is actually behind the mirror — we see the light coming from a direction determined by the law of reflection. The angles are such that our image appears exactly the same distance behind the mirror as we stand away from the mirror.

$light travelling along a normal is dash refracted$

Mirror Reflection : An image in a mirror appears as though it is behind the mirror. The two rays shown are those that strike the mirror at just the correct angles to be reflected into the eyes of the viewer. The image appears to come from the direction the rays are coming from when they enter the viewer’s eyes.

$light travelling along a normal is dash refracted$

Law of Reflection : The law of reflection states that the angle of reflection equals the angle of incidence: θr = θi. The angles are measured relative to the perpendicular to the surface at the point where the ray strikes the surface.

We expect to see reflections off a smooth surface. However, light strikes different parts of a rough surface at different angles, and it is reflected in many different directions (“diffused”). Diffused light is what allows us to see a sheet of paper from any angle. Many objects, such as people, clothing, leaves, and walls, have rough surfaces and can be seen from all sides. A mirror, on the other hand, has a smooth surface (compared with the wavelength of light) and reflects light at specific angles. When the moon reflects off the surface of a lake, a combination of these effects takes place.

Reflection : A brief overview of reflection and the law of reflection.

The Law of Refraction: Snell’s Law and the Index of Refraction

The amount that a light ray changes its direction depends both on the incident angle and the amount that the speed changes.

Formulate the relationship between the index of refraction and the speed of light

It is easy to notice some odd things when looking into a fish tank. For example, you may see the same fish appearing to be in two different places. This is because light coming from the fish to us changes direction when it leaves the tank, and in this case, it can travel two different paths to get to our eyes. The changing of a light ray’s direction (loosely called bending) when it passes through variations in matter is called refraction. Refraction is responsible for a tremendous range of optical phenomena, from the action of lenses to voice transmission through optical fibers.

$light travelling along a normal is dash refracted$

Law of Refraction : Looking at the fish tank as shown, we can see the same fish in two different locations, because light changes directions when it passes from water to air. In this case, the light can reach the observer by two different paths, and so the fish seems to be in two different places. This bending of light is called refraction and is responsible for many optical phenomena.

Refraction: The changing of a light ray’s direction (loosely called bending) when it passes through variations in matter is called refraction.

Speed of Light

The speed of light c not only affects refraction, it is one of the central concepts of Einstein’s theory of relativity. The speed of light varies in a precise manner with the material it traverses. It makes connections between space and time and alters our expectations that all observers measure the same time for the same event, for example. The speed of light is so important that its value in a vacuum is one of the most fundamental constants in nature as well as being one of the four fundamental SI units.

Why does light change direction when passing from one material ( medium ) to another? It is because light changes speed when going from one material to another.

Law of Refraction

A ray of light changes direction when it passes from one medium to another. As before, the angles are measured relative to a perpendicular to the surface at the point where the light ray crosses it. The change in direction of the light ray depends on how the speed of light changes. The change in the speed of light is related to the indices of refraction of the media involved. In mediums that have a greater index of refraction the speed of light is less. Imagine moving your hand through the air and then moving it through a body of water. It is more difficult to move your hand through the water, and thus your hand slows down if you are applying the same amount of force. Similarly, light travels slower when moving through mediums that have higher indices of refraction.

The amount that a light ray changes its direction depends both on the incident angle and the amount that the speed changes. For a ray at a given incident angle, a large change in speed causes a large change in direction, and thus a large change in angle. The exact mathematical relationship is the law of refraction, or “Snell’s Law,” which is stated in equation form as:

\[\mathrm{n_1 \sin \theta _1 = n_2 \sin \theta _2}\]

Here n 1 and n 2 are the indices of refraction for medium 1 and 2, and θ 1 and θ 2 are the angles between the rays and the perpendicular in medium 1 and 2. The incoming ray is called the incident ray and the outgoing ray the refracted ray, and the associated angles the incident angle and the refracted angle. The law of refraction is also called Snell’s law after the Dutch mathematician Willebrord Snell, who discovered it in 1621. Snell’s experiments showed that the law of refraction was obeyed and that a characteristic index of refraction n could be assigned to a given medium.

Understanding Snell’s Law with the Index of Refraction : This video introduces refraction with Snell’s Law and the index of refraction.The second video discusses total internal reflection (TIR) in detail. http://www.youtube.com/watch?v=fvrvqm3Erzk

Total Internal Reflection and Fiber Optics

Total internal reflection happens when a propagating wave strikes a medium boundary at an angle larger than a particular critical angle.

Formulate conditions required for the total internal reflection

Total internal reflection is a phenomenon that happens when a propagating wave strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is greater than the critical angle, the wave cannot pass through and is entirely reflected. The critical angle is the angle of incidence above which the total internal reflectance occurs.

What is Total Internal Reflection? : Describes the concept of total internal reflection, derives the equation for the critical angle and shows one example.

Critical angle

The critical angle is the angle of incidence above which total internal reflection occurs. The angle of incidence is measured with respect to the normal at the refractive boundary (see diagram illustrating Snell’s law ). Consider a light ray passing from glass into air. The light emanating from the interface is bent towards the glass. When the incident angle is increased sufficiently, the transmitted angle (in air) reaches 90 degrees. It is at this point no light is transmitted into air. The critical angle θcθc is given by Snell’s law, n1sinθ1=n2sinθ2n1sin⁡θ1=n2sin⁡θ2. Here, n 1 and n 2 are refractive indices of the media, and θ1θ1 and θ2θ2are angles of incidence and refraction, respectively. To find the critical angle, we find the value for θ1θ1 when θ2θ2= 90° and thus sinθ2=1sin⁡θ2=1. The resulting value of θ1θ1 is equal to the critical angle θc=θ1=arcsin(n2n1)θc=θ1=arcsin⁡(n2n1). So the critical angle is only defined when n 2 /n 1 is less than 1.

$light travelling along a normal is dash refracted$

Fig 1 : Refraction of light at the interface between two media, including total internal reflection.

Optical Fiber

Total internal reflection is a powerful tool since it can be used to confine light. One of the most common applications of total internal reflection is in fibre optics. An optical fibre is a thin, transparent fibre, usually made of glass or plastic, for transmitting light. The construction of a single optical fibre is shown in.

$light travelling along a normal is dash refracted$

Fig 2 : Fibers in bundles are clad by a material that has a lower index of refraction than the core to ensure total internal reflection, even when fibers are in contact with one another. This shows a single fiber with its cladding.

The basic functional structure of an optical fiber consists of an outer protective cladding and an inner core through which light pulses travel. The overall diameter of the fiber is about 125 μm and that of the core is just about 50 μm. The difference in refractive index of the cladding and the core allows total internal reflection in the same way as happens at an air-water surface show in. If light is incident on a cable end with an angle of incidence greater than the critical angle then the light will remain trapped inside the glass strand. In this way, light travels very quickly down the length of the cable over a very long distance (tens of kilometers). Optical fibers are commonly used in telecommunications, because information can be transported over long distances, with minimal loss of data. Another common use can be found in medicine in endoscopes. The field of applied science and engineering concerned with the design and application of optical fibers are called fiber optics.

Total Polarization

Brewster’s angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a surface.

Calculate the Brewster’s angle from the indices of refraction and discuss its physical mechanism

Brewster’s angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. This special angle of incidence is named after the Scottish physicist Sir David Brewster (1781–1868).

The physical mechanism for this can be qualitatively understood from the manner in which electric dipoles in the media respond to p-polarized light (whose electric field is polarized in the same plane as the incident ray and the surface normal). One can imagine that light incident on the surface is absorbed, and then re-radiated by oscillating electric dipoles at the interface between the two media. The refracted light is emitted perpendicular to the direction of the dipole moment; no energy can be radiated in the direction of the dipole moment. Thus, if the angle of reflection θ 1 (angle of reflection) is equal to the alignment of the dipoles (90 – θ 2 ), where θ 2 is angle of refraction, no light is reflected.

$light travelling along a normal is dash refracted$

Fig 1 : An illustration of the polarization of light that is incident on an interface at Brewster’s angle.

This geometric condition can be expressed as $\theta _ { 1 } + \theta _ { 2 } = 90 ^ { \circ }$, where θ 1 is the angle of incidence and θ 2 is the angle of refraction. Using Snell’s law (n 1 sinθ1 = n 2 sinθ 2 ), one can calculate the incident angle θ 1 = B at which no light is reflected: $\mathrm { n } _ { 1 } \sin \left( \theta _ { \mathrm { B } } \right) = \mathrm { n } _ { 2 } \sin \left( 90 ^ { \circ } - \theta _ { \mathrm { B } } \right)$ Solving for θ B gives $\theta _ { \mathrm { B } } = \arctan \left( \frac { \mathrm { n } _ { 2 } } { \mathrm { n } _ { 1 } } \right)$.

When light hits a surface at a Brewster angle, reflected beam is linearly polarized. shows an example, where the reflected beam was nearly perfectly polarized and hence, blocked by a polarizer on the right picture. Polarized sunglasses use the same principle to reduce glare from the sun reflecting off horizontal surfaces such as water or road.

$light travelling along a normal is dash refracted$

Fig 2 : Photograph taken of a window with a camera polarizer filter rotated to two different angles. In the picture at left, the polarizer is aligned with the polarization angle of the window reflection. In the picture at right, the polarizer has been rotated 90° eliminating the heavily polarized reflected sunlight.

Polarization Experience : A polarizing filter allows light of a particular plane of polarization to pass, but scatters the rest of the light. When two polarizing filters are crossed, almost no light gets through. Some materials have molecules that rotate the plane of polarization of light. When one of these materials is placed between crossed polarizing filters, more light is allowed to pass through.

Dispersion: Rainbows and Prisims

Dispersion is defined as the spreading of white light into its full spectrum of wavelengths.

Describe production of rainbows by a combination of refraction and reflection processes

We see about six colors in a rainbow—red, orange, yellow, green, blue, and violet; sometimes indigo is listed, too. These colors are associated with different wavelengths of light. White light, in particular, is a fairly uniform mixture of all visible wavelengths. Sunlight, considered to be white, actually appears to be a bit yellow because of its mixture of wavelengths, but it does contain all visible wavelengths. The sequence of colors in rainbows is the same sequence as the colors plotted versus wavelength. What this implies is that white light is spread out according to wavelength in a rainbow. Dispersion is defined as the spreading of white light into its full spectrum of wavelengths. More technically, dispersion occurs whenever there is a process that changes the direction of light in a manner that depends on wavelength. Dispersion, as a general phenomenon, can occur for any type of wave and always involves wavelength-dependent processes.

$light travelling along a normal is dash refracted$

Colors of a Rainbow : Even though rainbows are associated with seven colors, the rainbow is a continuous distribution of colors according to wavelengths.

Refraction is responsible for dispersion in rainbows and many other situations. The angle of refraction depends on the index of refraction, as we saw in the Law of Refraction. We know that the index of refraction n depends on the medium. But for a given medium, n also depends on wavelength. Note that, for a given medium, n increases as wavelength decreases and is greatest for violet light. Thus violet light is bent more than red light and the light is dispersed into the same sequence of wavelengths.

$light travelling along a normal is dash refracted$

Pure Light and Light Dispersion : (a) A pure wavelength of light falls onto a prism and is refracted at both surfaces. (b) White light is dispersed by the prism (shown exaggerated). Since the index of refraction varies with wavelength, the angles of refraction vary with wavelength. A sequence of red to violet is produced, because the index of refraction increases steadily with decreasing wavelength.

Rainbows are produced by a combination of refraction and reflection. You may have noticed that you see a rainbow only when you look away from the sun. Light enters a drop of water and is reflected from the back of the drop. The light is refracted both as it enters and as it leaves the drop. Since the index of refraction of water varies with wavelength, the light is dispersed, and a rainbow is observed. (There is no dispersion caused by reflection at the back surface, since the law of reflection does not depend on wavelength. ) The actual rainbow of colors seen by an observer depends on the myriad of rays being refracted and reflected toward the observer’s eyes from numerous drops of water. The arc of a rainbow comes from the need to be looking at a specific angle relative to the direction of the sun.

$light travelling along a normal is dash refracted$

Light Reflecting on Water Droplet : Part of the light falling on this water drop enters and is reflected from the back of the drop. This light is refracted and dispersed both as it enters and as it leaves the drop.

Light strikes different parts of a rough surface at different angles and is reflected, or diffused, in many different directions.
A mirror has a smooth surface (compared with the wavelength of light) and so reflects light at specific angles.
We see the light reflected off a mirror coming from a direction determined by the law of reflection.
The changing of a light ray’s direction (loosely called bending) when it passes through variations in matter is called refraction.
The index of refraction is n=c/v, where v is the speed of light in the material, c is the speed of light in vacuum, and n is the index of refraction.
Snell’s law, the law of refraction, is stated in equation form as n1sinθ1=n2sinθ2n1sin⁡θ1=n2sin⁡θ2.
The critical angle is the angle of incidence above which total internal reflection occurs and given as θc=arcsin(n2n1)θc=arcsin⁡(n2n1).
The critical angle is only defined when n2/n1 is less than 1.
If light is incident on an optical fiber with an angle of incidence greater than the critical angle then the light will remain trapped inside the glass strand. Light can travel over a very long distance without a significant loss.
When light hits a surface at a Brewster angle, reflected beam is linearly polarized.
The physical mechanism for the Brewster’s angle can be qualitatively understood from the manner in which electric dipoles in the media respond to p-polarized light.
Brewsters’ angle is given as θB=arctan(n2n1)θB=arctan⁡(n2n1).
Dispersion occurs whenever there is a process that changes the direction of light in a manner that depends on wavelength. Dispersion can occur for any type of wave and always involves wavelength-dependent processes.
For a given medium, n increases as wavelength decreases and is greatest for violet light. Thus violet light is bent more than red light, as can be seen with a prism.
In a rainbow, light enters a drop of water and is reflected from the back of the drop. The light is refracted both as it enters and as it leaves the drop.
reflection : the property of a propagated wave being thrown back from a surface (such as a mirror)
refraction : Changing of a light ray’s direction when it passes through variations in matter.
index of refraction : For a material, the ratio of the speed of light in vacuum to that in the material.
Snell’s law : A formula used to describe the relationship between the angles of incidence and refraction.
cladding : One or more layers of materials of lower refractive index, in intimate contact with a core material of higher refractive index.
dipole : A separation of positive and negative charges.
dielectric : An electrically insulating or nonconducting material considered for its electric susceptibility (i.e., its property of polarization when exposed to an external electric field).
polarizer : An optical filter that passes light of a specific polarization and blocks waves of other polarizations.

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Understanding Snell's Law with the Index of Refraction. Located at : http://www.youtube.com/watch?v=s6IGWO3e2Wo . License : Public Domain: No Known Copyright . License Terms : Standard YouTube license
Free High School Science Texts Project, Geometrical Optics: Total Internal Reflection. September 17, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m40070/latest/ . License : CC BY: Attribution
Fiber optics. Provided by : Wikipedia. Located at : http://en.Wikipedia.org/wiki/Fiber_optics . License : CC BY-SA: Attribution-ShareAlike
Total internal reflection. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Total_internal_reflection . License : CC BY-SA: Attribution-ShareAlike
cladding. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/cladding . License : CC BY-SA: Attribution-ShareAlike
Snell's law. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Snell's%20law . License : CC BY-SA: Attribution-ShareAlike
OpenStax College, Total Internal Reflection. January 29, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m42462/latest/ . License : CC BY: Attribution
Total internal reflection. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Total_internal_reflection . License : CC BY: Attribution
What is Total Internal Reflection?. Located at : http://www.youtube.com/watch?v=NXGLBMTtk40 . License : Public Domain: No Known Copyright . License Terms : Standard YouTube license
Brewster's angle. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Brewster's_angle . License : CC BY-SA: Attribution-ShareAlike
dipole. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/dipole . License : CC BY-SA: Attribution-ShareAlike
polarizer. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/polarizer . License : CC BY-SA: Attribution-ShareAlike
dielectric. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/dielectric . License : CC BY-SA: Attribution-ShareAlike
Polarization Experience. Located at : http://www.youtube.com/watch?v=Qv7Y-Er7rgc . License : Public Domain: No Known Copyright . License Terms : Standard YouTube license
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16.1 Reflection

Section learning objectives.

By the end of this section, you will be able to do the following:

Explain reflection from mirrors, describe image formation as a consequence of reflection from mirrors, apply ray diagrams to predict and interpret image and object locations, and describe applications of mirrors
Perform calculations based on the law of reflection and the equations for curved mirrors

Teacher Support

The learning objectives in this section help your students master the following standards:

(D) investigate behaviors of waves, including reflection, refraction, diffraction, interference, resonance, and the Doppler effect;
(E) describe and predict image formation as a consequence of reflection from a plane mirror and refraction through a thin convex lens; and
(F) describe the role of wave characteristics and behaviors in medical and industrial applications.

In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Mirrors and Lenses, as well as the following standards:

(D) investigate behaviors of waves, including reflection, refraction, diffraction, interference, resonance, and the Doppler effect.

Section Key Terms

Characteristics of mirrors.

[BL] Recall that, in geometry, angles are numbers that tell how far two straight lines are spread apart. The lines must be straight lines for the number to have meaning.

[OL] Geometry is the study of relationships involving points, lines, angles, and shapes. In this chapter, we are focused on the first three ideas.

[AL] In this chapter, we apply equations that use trigonometric functions that describe the properties of angles. Trigonometric functions are ratios of the lengths of two sides of a right triangle. There are six possible ratios; therefore, there are six such functions.

There are three ways, as shown in Figure 16.2 , in which light can travel from a source to another location. It can come directly from the source through empty space, such as from the Sun to Earth. Light can travel to an object through various media, such as air and glass. Light can also arrive at an object after being reflected, such as by a mirror. In all these cases, light is modeled as traveling in a straight line, called a ray . Light may change direction when it encounters the surface of a different material (such as a mirror) or when it passes from one material to another (such as when passing from air into glass). It then continues in a straight line—that is, as a ray. The word ray comes from mathematics. Here it means a straight line that originates from some point. It is acceptable to visualize light rays as laser rays (or even science fiction depictions of ray guns ).

Because light moves in straight lines, that is, as rays, and changes directions when it interacts with matter, it can be described through geometry and trigonometry. This part of optics, described by straight lines and angles, is therefore called geometric optics . There are two laws that govern how light changes direction when it interacts with matter: the law of reflection , for situations in which light bounces off matter; and the law of refraction , for situations in which light passes through matter. In this section, we consider the geometric optics of reflection .

[BL] Explain that light bounces is a simplification. The geometry of the path of a bouncing ball is similar to that of light, but what happens at the point of impact is different at the molecular level.

[OL] Indicate that the terms right angle , perpendicular , and normal line all mean the same thing: a vertical line at a 90° angle to a flat surface.

[AL] Recount and explain all the possible interactions of light with matter. Light can be absorbed at the surface of an opaque object. Some colors of light may be absorbed and others reflected. Light often is partially absorbed and partially reflected. It may also be transmitted through a transparent material, such as water or glass. Typically, if the surface of a transparent material is smooth, such as that of a window pane, light is transmitted partially and reflected partially.

Whenever we look into a mirror or squint at sunlight glinting from a lake, we are seeing a reflection. How does the reflected light travel from the object to your eyes? The law of reflection states: The angle of reflection , θ r θ r , equals the angle of incidence , θ i θ i . This law governs the behavior of all waves when they interact with a smooth surface, and therefore describe the behavior of light waves as well. The reflection of light is simplified when light is treated as a ray. This concept is illustrated in Figure 16.3 , which also shows how the angles are measured relative to the line perpendicular to the surface at the point where the light ray strikes it. This perpendicular line is also called the normal line , or just the normal . Light reflected in this way is referred to as specular (from the Latin word for mirror : speculum ).

We expect to see reflections from smooth surfaces, but Figure 16.4 , illustrates how a rough surface reflects light. Because the light is reflected from different parts of the surface at different angles, the rays go in many different directions, so the reflected light is diffused . Diffused light allows you to read a printed page from almost any angle because some of the rays go in different directions. Many objects, such as people, clothing, leaves, and walls, have rough surfaces and can be seen from many angles. A mirror, on the other hand, has a smooth surface and reflects light at specific angles.

When we see ourselves in a mirror, it appears that our image is actually behind the mirror. We see the light coming from a direction determined by the law of reflection. The angles are such that our image is exactly the same distance behind the mirror, d i , as the distance we stand away from the mirror, d o . Although these mirror images make objects appear to be where they cannot be (such as behind a solid wall), the images are not figments of our imagination. Mirror images can be photographed and videotaped by instruments and look just as they do to our eyes, which are themselves optical instruments. An image in a mirror is said to be a virtual image , as opposed to a real image . A virtual image is formed when light rays appear to diverge from a point without actually doing so.

Figure 16.5 helps illustrate how a flat mirror forms an image. Two rays are shown emerging from the same point, striking the mirror, and reflecting into the observer’s eye. The rays can diverge slightly, and both still enter the eye. If the rays are extrapolated backward, they seem to originate from a common point behind the mirror, allowing us to locate the image. The paths of the reflected rays into the eye are the same as if they had come directly from that point behind the mirror. Using the law of reflection—the angle of reflection equals the angle of incidence—we can see that the image and object are the same distance from the mirror. This is a virtual image, as defined earlier.

Fun In Physics

Mirror mazes.

Figure 16.6 is a chase scene from an old silent film called The Circus , starring Charlie Chaplin. The chase scene takes place in a mirror maze. You may have seen such a maze at an amusement park or carnival. Finding your way through the maze can be very difficult. Keep in mind that only one image in the picture is real—the others are virtual.

One of the earliest uses of mirrors for creating the illusion of space is seen in the Palace of Versailles, the former home of French royalty. Construction of the Hall of Mirrors ( Figure 16.7 ) began in 1678. It is still one of the most popular tourist attractions at Versailles.

Grasp Check

Only one Charlie in this image ( Figure 16.8 ) is real. The others are all virtual images of him. Can you tell which is real? Hint—His hat is tilted to one side.

The virtual images have their hats tilted to the right.
The virtual images have their hats tilted to the left.
The real images have their hats tilted to the right.
The real images have their hats tilted to the left.

Watch Physics

Virtual image.

This video explains the creation of virtual images in a mirror. It shows the location and orientation of the images using ray diagrams, and relates the perception to the human eye.

The distances of the image and the object from the mirror are the same.
The distances of the image and the object from the mirror are always different.
The image is formed at infinity if the object is placed near the mirror.
The image is formed near the mirror if the object is placed at infinity.

Have students construct a ray diagram for an object reflected in a plane mirror. Point out to them that all information can be represented in the diagram by using just paper, a pencil, a ruler, and a protractor. Students may use the preceding video and Figure 16.5 to help them to draw the necessary rays for the diagram. Have them compare the position and orientation of the virtual image with that of the object, paying particular attention to the identical distances that the object and image have with respect to the mirror surface.

Misconception Alert

[BL] Ask students to define virtual and dispel any misconceptions. Explain the term in relation to geometric optics.

[OL] Explain that a real focal point is a point at which there is a concentration of light energy that can be transformed into other useful forms. At a virtual focal point , on the other hand, light energy cannot be concentrated because no light actually goes to that point.

[AL] Explain the difference between a parabolic shape and a spherical shape. Use drawings of a cross-section of each. Point out that, for a short section of a curved mirror with very little curvature, a spherical mirror approximates a parabolic one.

Some mirrors are curved instead of flat. A mirror that curves inward is called a concave mirror , whereas one that curves outward is called a convex mirror . Pick up a well-polished metal spoon and you can see an example of each type of curvature. The side of the spoon that holds the food is a concave mirror; the back of the spoon is a convex mirror. Observe your image on both sides of the spoon.

Tips For Success

You can remember the difference between concave and convex by thinking, Concave means caved in .

Ray diagrams can be used to find the point where reflected rays converge or appear to converge, or the point from which rays appear to diverge. This is called the focal point , F. The distance from F to the mirror along the central axis (the line perpendicular to the center of the mirror’s surface) is called the focal length , f . Figure 16.9 shows the focal points of concave and convex mirrors.

Images formed by a concave mirror vary, depending on which side of the focal point the object is placed. For any object placed on the far side of the focal point with respect to the mirror, the rays converge in front of the mirror to form a real image, which can be projected onto a surface, such as a screen or sheet of paper However, for an object located inside the focal point with respect to the concave mirror, the image is virtual. For a convex mirror the image is always virtual—that is, it appears to be behind the mirror. The ray diagrams in Figure 16.10 show how to determine the nature of the image formed by concave and convex mirrors.

The information in Figure 16.10 is summarized in Table 16.1 .

Concave and Convex Mirrors

Silver spoon and silver polish, or a new spoon made of any shiny metal

Instructions

Choose any small object with a top and a bottom, such as a short nail or tack, or a coin, such as a quarter. Observe the object’s reflection on the back of the spoon.
Observe the reflection of the object on the front (bowl side) of the spoon when held away from the spoon at a distance of several inches.
Observe the image while slowly moving the small object toward the bowl of the spoon. Continue until the object is all the way inside the bowl of the spoon.
You should see one point where the object disappears and then reappears. This is the focal point.

Describe the differences in the image of the object on the two sides of the focal point. Explain the change. Identify which of the images you saw were real and which were virtual.

The height of the image became infinite.
The height of the object became zero.
The intensity of intersecting light rays became zero.
The intensity of intersecting light rays increased.

[BL] [OL] Ask students to identify as many examples as they can of curved mirrors that are used in everyday applications. Supply any they miss: security mirrors, mirrors for entering and exiting a driveway with poor visibility, rear-view mirrors, mirrors for application of cosmetics, and so on.

Parabolic Mirrors and Real Images

This video uses ray diagrams to show the special feature of parabolic mirrors that makes them ideal for either projecting light energy in parallel rays, with the source being at the focal point of the parabola, or for collecting at the focal point light energy from a distant source.

The rays do not polarize after reflection.
The rays are dispersed after reflection.
The rays are polarized after reflection.
The rays become parallel after reflection.

Teacher Demonstration

Have students use the demonstration in the video to construct a ray diagram that shows that rays from an object (upright arrow) placed at the focal point of a concave mirror emerge parallel to the central axis.

You should be able to notice everyday applications of curved mirrors. One common example is the use of security mirrors in stores, as shown in Figure 16.11 .

Some telescopes also use curved mirrors and no lenses (except in the eyepieces) both to magnify images and to change the path of light. Figure 16.12 shows a Schmidt-Cassegrain telescope. This design uses a spherical primary concave mirror and a convex secondary mirror. The image is projected onto the focal plane by light passing through the perforated primary mirror. The effective focal length of such a telescope is the focal length of the primary mirror multiplied by the magnification of the secondary mirror. The result is a telescope with a focal length much greater than the length of the telescope itself.

A parabolic concave mirror has the very useful property that all light from a distant source, on reflection by the mirror surface, is directed to the focal point. Likewise, a light source placed at the focal point directs all the light it emits in parallel lines away from the mirror. This case is illustrated by the ray diagram in Figure 16.13 . The light source in a car headlight, for example, is located at the focal point of a parabolic mirror.

Parabolic mirrors are also used to collect sunlight and direct it to a focal point, where it is transformed into heat, which in turn can be used to generate electricity. This application is shown in Figure 16.14 .

The Application of the Curved Mirror Equations

[BL] [OL] Review operations for manipulating fractions and for rearranging equations involving fractional values of variables.

[AL] Demonstrate how to solve equations of the type 1 a = 1 b + 1 c 1 a = 1 b + 1 c for any of the variables in terms of the other two. Rearrange so that the variable solved for is not a reciprocal.

Curved mirrors and the images they create involve a fairly small number of variables: the mirror’s radius of curvature, R ; the focal length, f ; the distances of the object and image from the mirror, d o and d i , respectively; and the heights of the object and image, h o and h i , respectively. The signs of these values indicate whether the image is inverted, erect (upright), real, or virtual. We now look at the equations that relate these variables and apply them to everyday problems.

Figure 16.15 shows the meanings of most of the variables we will use for calculations involving curved mirrors.

The basic equation that describes both lenses and mirrors is the lens/mirror equation

This equation can be rearranged several ways. For example, it may be written to solve for focal length.

Magnification, m , is the ratio of the size of the image, h i , to the size of the object, h o . The value of m can be calculated in two ways.

This relationship can be written to solve for any of the variables involved. For example, the height of the image is given by

We saved the simplest equation for last. The radius of curvature of a curved mirror, R , is simply twice the focal length.

We can learn important information from the algebraic sign of the result of a calculation using the previous equations:

A negative d i indicates a virtual image; a positive value indicates a real image
A negative h i indicates an inverted image; a positive value indicates an erect image
For concave mirrors, f is positive; for convex mirrors, f is negative

Now let’s apply these equations to solve some problems.

Worked Example

Calculating focal length.

A person standing 6.0 m from a convex security mirror forms a virtual image that appears to be 1.0 m behind the mirror. What is the focal length of the mirror?

The person is the object, so d o = 6.0 m. We know that, for this situation, d o is positive. The image is virtual, so the value for the image distance is negative, so d i = –1.0 m.

Now, use the appropriate version of the lens/mirror equation to solve for focal length by substituting the known values.

f = d i d o d o + d i = ( − 1.0 ) ( 6.0 ) 6.0 + ( − 1.0 ) = − 6.0 5.0 = − 1.2 m f = d i d o d o + d i = ( − 1.0 ) ( 6.0 ) 6.0 + ( − 1.0 ) = − 6.0 5.0 = − 1.2 m

The negative result is expected for a convex mirror. This indicates the focal point is behind the mirror.

Calculating Object Distance

Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR radiation follows the same law of reflection as visible light. Given that the mirror has a radius of curvature of 50.0 cm and produces an image of the coils 3.00 m in front of the mirror, where are the coils with respect to the mirror?

We are told that the concave mirror projects a real image of the coils at an image distance d i = 3.00 m. The coils are the object, and we are asked to find their location—that is, to find the object distance d o . We are also given the radius of curvature of the mirror, so that its focal length is f = R /2 = 25.0 cm (a positive value, because the mirror is concave, or converging). We can use the lens/mirror equation to solve this problem.

Because d i and f are known, the lens/mirror equation can be used to find d o .

Rearranging to solve for d o , we have

Entering the known quantities gives us

Note that the object (the coil filament) is farther from the mirror than the mirror’s focal length. This is a case 1 image ( d o > f and f positive), consistent with the fact that a real image is formed. You get the most concentrated thermal energy directly in front of the mirror and 3.00 m away from it. In general, this is not desirable because it could cause burns. Usually, you want the rays to emerge parallel, and this is accomplished by having the filament at the focal point of the mirror.

Note that the filament here is not much farther from the mirror than the focal length, and that the image produced is considerably farther away.

Practice Problems

What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away? Construct a ray diagram using paper, a pencil and a ruler to confirm your calculation.

Check Your Understanding

Use these questions to assess student achievement of the section’s learning objectives. If students are struggling with a specific objective, these questions will help identify which one, and then you can direct students to the relevant content.

How does the object distance, d o , compare with the focal length, f, for a concave mirror that produces an image that is real and inverted?

d o > f, where d o and f are object distance and focal length, respectively.
d o < f, where d o and f are object distance and focal length, respectively.
d o = f, where do and f are object distance and focal length, respectively.
d o = 0, where do is the object distance.

Use the law of reflection to explain why it is not a good idea to polish a mirror with coarse sandpaper.

The surface becomes smooth. A smooth surface produces a sharp image.
The surface becomes irregular. An irregular surface produces a sharp image.
The surface becomes smooth. A smooth surface transmits but does not reflect light.
The surface becomes irregular. An irregular surface produces a blurred image.
It is real and erect.
It is real and inverted.
It is virtual and inverted.
It is virtual and erect.

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Book title: Physics
Publication date: Mar 26, 2020
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Section URL: https://openstax.org/books/physics/pages/16-1-reflection

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$light travelling along a normal is dash refracted$

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$light travelling along a normal is dash refracted$

The Amount of Bending

The amount of bending that a light ray experiences can be expressed in terms of the angle of refraction (more accurately, by the difference between the angle of refraction and the angle of incidence). A ray of light may approach the boundary at an angle of incidence of 45-degrees and bend towards the normal. If the medium into which it enters causes a small amount of refraction, then the angle of refraction might be a value of about 42-degrees. On the other hand if the medium into which the light enters causes a large amount of refraction, the angle of refraction might be 22-degrees. (These values are merely arbitrarily chosen values to illustrate a point.) The diagram below depicts a ray of light approaching three different boundaries at an angle of incidence of 45-degrees. The refractive medium is different in each case, causing different amounts of refraction. The angles of refraction are shown on the diagram.

Of the three boundaries in the diagram, the light ray refracts the most at the air-diamond boundary. This is evident by the fact that the difference between the angle of incidence and the angle of refraction is greatest for the air-diamond boundary. But how can this be explained? The cause of refraction is a change in light speed; and wherever the light speed changes most, the refraction is greatest. We have already learned that the speed is related to the optical density of a material that is related to the index of refraction of a material. Of the four materials present in the above diagram, air is the least dense material (lowest index of refraction value) and diamond is the most dense material (largest index of refraction value). Thus, it would be reasonable that the most refraction occurs for the transmission of light across an air-diamond boundary.

In this example, the angle of refraction is the measurable quantity that indicates the amount of refraction taking place at any boundary. A comparison of the angle of refraction to the angle of incidence provides a good measure of the refractive ability of any given boundary. For any given angle of incidence, the angle of refraction is dependent upon the speeds of light in each of the two materials. The speed is in turn dependent upon the optical density and the index of refraction values of the two materials. There is a mathematical equation relating the angles that the light rays make with the normal to the indices (plural for index) of refraction of the two materials on each side of the boundary. This mathematical equation is known as Snell's Law and is the topic of the next section of Lesson 2 .

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Light, which is travelling along a normal, is ............ refracted
Q 4. A ray of light travelling in water falls at right angles to the boundary of a parallel-sided glass block. The ray of light : (a) is refracted towards the normal (b) is refracted away from the normal (c) does not get refracted (d) is reflected along the same path. View Solution. Q 5.
Refraction and light bending (article)
Because the light can't travel as quickly in the water as it does in the air, the light bends around the pencil, causing it to look bent in the water. Basically, the light refraction gives the pencil a slight magnifying effect, which makes the angle appear bigger than it actually is, causing the pencil to look crooked.
Why a light ray does not refract when it is incident normally to the
The reason that the light is not refracting is that it will take the path that will take the shortest time from through the medium. This is essentially what snell's law gives us. Since, we are looking at light at normal incidence there is no path that will take shorter time than to continue straight forward in the same medium.
Physics Tutorial: Snell's Law of Refraction
The angle of incidence in the water is approximately 39°. At this angle, the light refracts out of the water into the surrounding air bending away from the normal. The angle of refraction in the air is approximately 57°. These values for the angle of incidence and refraction are consistent with Snell's Law.
11.4: The Law of Refraction
Summary. The changing of a light ray's direction when it passes through variations in matter is called refraction. The speed of light in vacuuum c = 2.99792458 × 108 ∼ 3.00 × 108m / s. Index of refraction n = c v, where v is the speed of light in the material, c is the speed of light in vacuum, and n is the index of refraction.
10.4: Refraction
The amount that the direction of the light ray changes when the wave enters a new medium depends upon how much the wave slows down or speeds up upon changing media. The property of the medium which determines the speed of light is known as its index of refraction, n n, and is defined as: n = c v (10.4.1) (10.4.1) n = c v.
Snell's Law
Question: A ray of light travelling in air falls on the surface of a transparent glass slab. The ray makes and angle of $45^{\circ}$ with the normal to the surface. Find the angle made by the refracted ray with the normal within the slab. Given that refractive index of the glass slab is $\sqrt{2}$.
Refraction Of Light
This phenomenon is known as apparent depth. The cause of this illusion is the refraction of light. Refraction occurs when light waves travel from one medium to another at an angle and change speed due to the difference in the optical density of the two media. This change in speed causes the light rays to bend.
Physics Tutorial: The Cause of Refraction
The Cause of Refraction. We have learned that refraction occurs as light passes across the boundary between two media. Refraction is merely one of several possible boundary behaviors by which a light wave could behave when it encounters a new medium or an obstacle in its path. The transmission of light across a boundary between two media is ...
Physics Tutorial: Refraction and the Ray Model of Light
Lenses serve to refract light at each boundary. As a ray of light enters a lens, it is refracted; and as the same ray of light exits the lens, it is refracted again. The net effect of the refraction of light at these two boundaries is that the light ray has changed directions. Because of the special geometric shape of a lens, the light rays are ...
Light
The law of refraction, or Snell's law, predicts the angle at which a light ray will bend, or refract, as it passes from one medium to another. (more) When light traveling in one transparent medium encounters a boundary with a second transparent medium (e.g., air and glass), a portion of the light is reflected and a portion is transmitted into ...
16.2 Refraction
The light is refracted both as it enters and as it leaves the drop. Because the index of refraction of water varies with wavelength, the light is dispersed and a rainbow is observed. Figure 16.19 Part of the light falling on this water drop enters and is reflected from the back of the drop.
Refraction Towards the Normal
An incident ray of light is refracted towards the normal and slows down when it travels from air into glass. Compared with air, glass is a slower, more optically dense medium (with the higher refractive index). An incident ray of light is refracted away from the normal and speeds up when it travels from glass into air. Compared with glass, air ...
25.3: The Law of Refraction
The equation for index of refraction (Equation 25.3.3) can be rearranged to determine v. v = c n. The index of refraction for zircon is given as 1.923 in Table 25.3.1, and c is given in the equation for speed of light. Entering these values in the last expression gives. v = 3.00 × 108m / s 1.923 = 1.56 × 108m / s.
Is it true to say no refraction takes place when a ray comes along
Resnick Halliday says: ""Travel of light through an interface is called refraction and the light is said to be refracted.Unless an incident beam of light is perpendicular to surface, refraction changes light's direction of travel "" From this can we conclude that Bending of light is a consequence of refraction but Bending of light itself is not ...
Reflection and refraction of light
If the ray meets the boundary at an angle to the normal, it bends away from the normal. The greater the change of speed of light at a boundary, the greater the refraction.
Physics Tutorial: Refraction and Sight
As light travels through a given medium, it travels in a straight line. However, when light passes from one medium into a second medium, the light path bends. Refraction takes place. The refraction occurs only at the boundary. Once the light has crossed the boundary between the two media, it continues to travel in a straight line.
Light, which is travelling along a normal, is ............ refracted
A beam of white light enters the curved surface of semicircular piece of glass along the normal. The incoming beams is moved clockwise (so that the angle θ increases), The color of the refracted beam is red before it steps energing from flat surface.
Refraction of Light
The refraction of light is the bending of light rays as they pass from one medium to another, thereby changing the path of the rays. Refraction occurs due to a change in the speed of the light ray or wave. [1] The speed of light is greatest in a vacuum. When the light rays travel from a rarer to a denser medium, they bend towards the normal. If the light rays travel from a denser to a rarer ...
24.2: Reflection, Refraction, and Dispersion
Speed of Light. The speed of light c not only affects refraction, it is one of the central concepts of Einstein's theory of relativity. The speed of light varies in a precise manner with the material it traverses. It makes connections between space and time and alters our expectations that all observers measure the same time for the same event, for example.
16.1 Reflection
There are three ways, as shown in Figure 16.2, in which light can travel from a source to another location. It can come directly from the source through empty space, such as from the Sun to Earth. Light can travel to an object through various media, such as air and glass. Light can also arrive at an object after being reflected, such as by a ...
Physics Tutorial: The Angle of Refraction
In such a case, the refracted ray will be farther from the normal line than the incident ray; this is the SFA rule of refraction. On the other hand, if a light wave passes from a medium in which it travels fast (relatively speaking) into a medium in which it travels slow, then the light wave will refract towards the normal. In such a case, the ...
A ray of light is travelling in a direction perpendicular to the
Is refracted towards the normal. Is refracted away from the normal. Is reflected along the same path. Does not get refracted. Advertisements. Solution Show Solution. A ray of light is travelling in a direction perpendicular to the boundary of a parallel glass slab. The ray of light does not get refracted.

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