When a ray of light incident normally on a surface of transparent medium refracted ray bends towards normal?

Edited by Sim, Jen Moreau

When a beam of light strikes the boundary separating two transparent media such as air and water or glass, some of the light is reflected whereas the remaining portion enters the second medium and undergoes a change in direction as well as in velocity. This change of direction and velocity of light is called refraction of light.

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Consider a surface A'B' which separates two media. When a ray of light AO passes from one medium to the other, its direction changes along OC instead of straight line AB. Point 'O' is the point of incidence, NO'N is the normal to the surface A'B'. OA is the incident ray and OC is the refracted ray. The angle AON = Li and the angle CON' =Lr. From this discussion and experiment, it is clear that "when a light passes from a rare to a dense medium, the refracted ray bends towards the normal and when a ray of light passes from dense to a rare medium, the refracted ray bends away from normal as shown below (Note: glass is denser than water and water is denser than air).

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Laws of Refraction:

There are two laws of refraction.

Mathematically, n= SinLi/SinLr

Index of Refraction:

When light passes from one medium into another, it is refracted, because the speed of light is different in different media. In general, the speed of light in any medium is less than the speed of light in vacuum. It is, therefore, convenient to define the index of refraction "n" as the ratio of the velocities of light in vacuum or air to the velocity of light in the given medium.

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n= velocity of light in air or vacuum/ velocity of light in medium

n= C/V, where C= 3x108m/s

Note: Since the speed of light in the vacuum is almost equal to the speed of light in air, we use the speed of light in the air instead of vacuum. The refractive index is a ratio of two similar quantities, therefore, having no unit. It only shows the ability of a substance to bend light rays. The refractive index of a substance depends only on the nature of the medium and wavelength and does not depend on the angle of incidence. Moreover, as the apparent depth of water pond seems less than its real depth, we can calculate the refractive index of water as,

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n= Real depth/ apparent depth

Ref: nwater=1.33 and nair= 1.0003

Total Internal Reflection:

When a beam of light passes through an optically denser medium to a rarer medium, i.e. from water to air, the refracted ray bends away from the normal, and the angle of refraction "Lr" is always greater than the corresponding angle of incidence. "Li"

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It should be noted that as the angle of incidence increases, the angle of refraction also increases until a certain value where the corresponding angle of refraction becomes 90º and the refracted ray runs along the surface (separating the two media). When the value of the angle of incidence becomes greater than the critical angle, there is no refraction and the whole ray is internally reflected in the medium, such a process is called total internal reflection.

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Critical Angle:

When the light enters from a denser medium to rarer medium, the value of the angle of incidence for which its corresponding angle of refraction is 90º is called critical angle. Li=Lie, when r= 90º

Conditions for Total Internal Reflection:

The following two conditions are necessary for total internal reflection.

If the critical angle for a specific medium is known, then the refractive index "n" can be found as n= 1/ sin ic

Proof:

The following are applications or examples of total internal reflection.

1. 1

2. 2

3. 3

4. 4

5. 5

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Comments

Categories : Physics

Recent edits by: Sim

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.

You can think of it as a life guard who is trying to save a person drowning in a river. If the river is flowing and the life guard will run towards the person at an angle(on land) and he takes the current into account as he is faster on land than in the water. Thus, having different angles on land and in the water. If the water is still and the person needing help is straight out from the shore the life guard will run in a straight line to the shore and then swim straight out to rescue the person in the water.

Snell's law can be derived from Fermat's Principle which is the statement that the light will take the path that uses the least time. See the wikipedia article Snell's law for the derivation of the formula.

as mentioned by Aaron since the $\theta_1$ is zero, thus $\sin(\theta_1)=0$, $\theta_2$ needs to be zero for Snell's law to be satisfied. Below is snell's law: $$n_1\sin(\theta _1)=n_2\sin(\theta _2)$$

It is also possible to derive this directly form Maxwell's equations but that would be a boring and time consuming task.

Also note that if we are going from a medium with higher refractive index to a medium with lower refractive index we can get a situation where we will need $sin(\theta_2)$ to be greater than 1, this will result in a total internal reflection where no light will pass trough the interface.

Refraction is the bending of light (it also happens with sound, water and other waves) as it passes from one transparent substance into another.

This bending by refraction makes it possible for us to have lenses, magnifying glasses, prisms and rainbows. Even our eyes depend upon this bending of light. Without refraction, we wouldn’t be able to focus light onto our retina.

Change of speed causes change of direction

Light refracts whenever it travels at an angle into a substance with a different refractive index (optical density).

This change of direction is caused by a change in speed. For example, when light travels from air into water, it slows down, causing it to continue to travel at a different angle or direction.

How much does light bend?

The amount of bending depends on two things:

• Change in speed – if a substance causes the light to speed up or slow down more, it will refract (bend) more.
• Angle of the incident ray – if the light is entering the substance at a greater angle, the amount of refraction will also be more noticeable. On the other hand, if the light is entering the new substance from straight on (at 90° to the surface), the light will still slow down, but it won’t change direction at all.

Refractive index of some transparent substances

All angles are measured from an imaginary line drawn at 90° to the surface of the two substances This line is drawn as a dotted line and is called the normal.

If light enters any substance with a higher refractive index (such as from air into glass) it slows down. The light bends towards the normal line.

If light travels enters into a substance with a lower refractive index (such as from water into air) it speeds up. The light bends away from the normal line.

A higher refractive index shows that light will slow down and change direction more as it enters the substance.

Lenses

A lens is simply a curved block of glass or plastic. There are two kinds of lens.

A biconvex lens is thicker at the middle than it is at the edges. This is the kind of lens used for a magnifying glass. Parallel rays of light can be focused in to a focal point. A biconvex lens is called a converging lens.

A biconcave lens curves is thinner at the middle than it is at the edges. Light rays refract outwards (spread apart) as they enter the lens and again as they leave.

Refraction can create a spectrum

Isaac Newton performed a famous experiment using a triangular block of glass called a prism. He used sunlight shining in through his window to create a spectrum of colours on the opposite side of his room.

This experiment showed that white light is actually made of all the colours of the rainbow. These seven colours are remembered by the acronym ROY G BIV – red, orange, yellow, green, blue, indigo and violet.

Newton showed that each of these colours cannot be turned into other colours. He also showed that they can be recombined to make white light again.

The explanation for the colours separating out is that the light is made of waves. Red light has a longer wavelength than violet light. The refractive index for red light in glass is slightly different than for violet light. Violet light slows down even more than red light, so it is refracted at a slightly greater angle.

The refractive index of red light in glass is 1.513. The refractive index of violet light is 1.532. This slight difference is enough for the shorter wavelengths of light to be refracted more.

Rainbows

A rainbow is caused because each colour refracts at slightly different angles as it enters, reflects off the inside and then leaves each tiny drop of rain.

A rainbow is easy to create using a spray bottle and the sunshine. The centre of the circle of the rainbow will always be the shadow of your head on the ground.

The secondary rainbow that can sometimes be seen is caused by each ray of light reflecting twice on the inside of each droplet before it leaves. This second reflection causes the colours on the secondary rainbow to be reversed. Red is at the top for the primary rainbow, but in the secondary rainbow, red is at the bottom.

Use these activities with your students to explore refration further:

• Investigating refraction and spearfishing – students aim spears at a model of a fish in a container of water. When they move their spears towards the fish, they miss!
• Angle of refraction calculator challenge – students choose two types of transparent substance. They then enter the angle of the incident ray in the spreadsheet calculator, and the angle of the refracted ray is calculated for them.
• Light and sight: true or false? – students participate in an interactive ‘true or false’ activity that highlights common alternative conceptions about light and sight. This activity can be done individually, in pairs or as a whole class.

Learn more about different types of rainbows, how they are made and other atmospheric optical phenomena with this MetService blog and Science Kids post.

Learn more about human lenses, optics, photoreceptors and neural pathways that enable vision through this tutorial from Biology Online.