Ray Optics and Optical Instruments

Refraction Through a Prism

Have you ever observed that the people standing in the pool always look shorter then they are? Also, the spoon in the glass of water appears to be bent. Why does this happen? This is because of refraction. Let us now study about ”refraction through a prism”.

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What is Refraction?

Before studying how refraction takes place through a prism, let us see what refraction is. The change in direction or bending of a light wave passing from one transparent medium to another caused by the change in wave’s speed is the refraction. The extent of bending of light rays entering from one medium to another is the refractive index and is denoted by the ‘n’.

It is represented as n = c/v, where c = velocity/speed of light of a certain wavelength in the air and v = velocity of light in any medium.

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What is a Prism?

It is a solid figure having two triangular bases and three rectangular surfaces and is the closed surface. The angle between each surface is the angle of the prism. Here the opposite surfaces are equal surfaces and are parallel.  We notice that here there are two refracting surfaces which means the surface where refraction of light takes place.

Learn more about Human eye and Defects of Vision here.

Refraction Through a Prism

Let A, B, C be the glass of the prism. Suppose BC is the base and AB and AC are its two refracting surfaces. From the above figure, we can say that OP is the incident. The ray traveling through the rarer medium and than the refractive index of the prism is the incident ray. As the ray PQ strikes the surface of the and it is called as the refracted ray. OR is the emergent ray which comes out.

When the ray light enters the glass, it bends towards normal and when ray comes out, it bends away from the normal. Now the angle between the emergent ray and incident ray is the angle of deviation. For a single refracting surface,  δ = |i – r|

In this case, δ = (i1 + i2) – (r1 + r2)

δ = i+ i2 – A, A is the angle between the prism between two lateral surfaces. We know that ∠A and ∠Q is 180º and Angle of the prism of (A) is r1 + r2

r1  is the angle of refraction inside the prism and ris the angle of refraction outside it. For an angle of minimum deviation, δ is minimum and i1 = i2 = i

δmin = 2i – A

For small A, δ = (µ – 1) A

Minimum Angle of Deviation for a Prism

At the minimum deviation, Dm the refracted ray inside the prism becomes parallel to its base, i.e. i = e ⇒ r1 = r2 = r, then r = A/2 and Dm = 2i – A, where i is the angle of emergence, r1 and r2 are the angles of refraction and A is the angle of the prism.

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Refraction Through a Prism

Learn more about Atmospheric Refraction and Scattering of Light here.

Question For You

Q. A prism made up of flint glass is such that the incident ray does not emerge from the second surface. The critical angle for flint glass is 36º. Then, refracting angle A must be

  1. 37º
  2. 54º
  3. 71º
  4. 73º

Answer: D. In the prism to occur the total internal reflection, the reflecting angle must be more than twice the critical angle of the material. So here the critical angle for flint glass is 36º so the refracting angle must be greater than 72.

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