Refraction of Light

4 Parts:

Applications of Total Internal Reflection

Refraction of Light through Prism

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Refraction of Light

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.

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).

Laws of Refraction:

There are two laws of refraction.

1. 1
   The incident ray, the refracted ray and the normal all lie in the same plane at the incident point

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2. 2
   The second law called Snell's law was discovered by Snell in 1621

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   According to this law, "The ratio of the sine of the angle of incidence "I" to the sine of the angle of refraction "r" is constant for all the rays of light passing from one medium to the other. This constant is called index of refraction.

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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.

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,

n= Real depth/ apparent depth

Ref: n_water=1.33 and n_air= 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"

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.

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.

1. 1
   The ray of light should travel from a denser to a less dense medium

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2. 2
   The angle of incidence should be greater than the critical angle

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Relation between Critical angle & Refractive Index:

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

Proof:

                           As    n= sin Li/sin Lr

                           Also, n= index of air/ index of medium

                           So,   sin Li/sin Lr= index of air/ index of medium

                           Sin ic/sin90= 1/ index of medium

                            Index= I/sin ic 

The following are applications or examples of total internal reflection.

1. 1
   Periscope

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   It is an instrument which enables the crew of a submarine to obtain information about a ship on the surface of the water when it is itself submerged into the water. In this device, two persons (totally reflected prisms, i.e one angle is 90º and two others 45º each) are used as shown in the figure below. Light entering and leaving each prism does not suffer refraction because <I=0. Light rays striking the hypotenuse side of the prism at an angle of 45º are totally internally reflected because the value of the critical angle of glass is 42º.

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2. 2
   Sparkling of Diamond

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   Sparkling of diamond is a very good example of total internal reflection because of a very high value 'n', the critical angle is very small, 24º. Hence when light enters the diamond particle, it is totally reflected many times inside the diamond.

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3. 3
   Endoscope

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   The endoscope is an optical instrument used to view & photograph the inside of a hollow organ. Such as the bladder, the stomach, etc. Using optical fibers in an endoscope, the part of the body to be viewed is illuminated. A video camera is fitted outside the bundles of optical fibers. This makes the interior part of the organ visible to the surgeon during an operation.

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4. 4
   Optical Fibers

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   An optical fiber is made up of a fine strand of glass coated with another type of glass of lower refractive index. A single fiber is about the thickness of human hair (0.01) mm. The light rays falling on the interface between two types of glasses undergo total internal reflection. Thus, when light enters one end of the fiber is refracted towards the normal by the inner glass. The refracted ray falls on the boundary between two types of glass and undergoes total internal reflection. After many repeated internal reflections at the walls, it emerges out at the other end as shown in the figure. If several thousands of these fibers are bonded together, a flexible light pipe is obtained that can be used by doctors and engineers to light up some inaccessible parts during an examination.

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5. 5
   The Binoculars

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   The binoculars also make use of prisms to reduce the length of the instrument and to produce an erect image. The light rays in a pair of binoculars are bent by180º through each prism in contrast to the periscope where light rays are only bent through 90º by each prism.

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Prism: Prism is a transparent body having three rectangular and two triangular surfaces. It is usually made of glass commonly used to separate light into its component wavelengths or spectral colors. When a ray of light enters the prism, it is bent twice, once during entering the prism and once during leaving.

Angle of Prism: The angle between the two refracting rectangular surfaces opposite to the base is called the angle of the prism. In the figure: the incident ray EF makes an angle EFO=Li with the surface AB. This ray, while entering the glass prism, bends towards the base of the prism BC. When this refracted ray 'FG' emerges out of the prism, it bends away from the normal. The emergent ray 'GH' deviates from its original path 'EFK'. If we produce 'GH' backward, it will meet ' EFK' at point 'O' making an angle KOH. This angle through which the emergent ray has deviated is called the angle of deviation 'D' i.e angle KOH. The minimum value of the angle of deviation is called angle of minimum deviation. The angle of deviation depends on the following factors:

1. 1
   Angle 'A' of the prism.

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2. 2
   The incident angle.

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3. 3
   The refractive index of the prism

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It is experimentally verified that when the refracted ray becomes parallel with the base 'BC' of the prism, then the angle of deviation 'Dm' becomes minimum. The index of refraction of the material of the prism can be determined by the relation

n= sin (A+Dm)/ Sin a/2

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