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Question

A light ray is incident on an equilateral prism of refractive index 2. What should be the angle of incidence such that the ray gazes on the second surface?

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Solution

Let's trace a path of incident light ray:


Anlge of prism (A) = 60o
A = r1 + r2 ..(1)
Emergent ray gazes at second surface means that ray incident at critical angle on the second surface.
Angle of emergent = 90o
Critical angle = r2

sin r2sin e=Refractive index of air(1)Refractive index of prism ..(2)

For the first surface;
sin θsin r1=21 ..(3)

For the second surface;
Usind 2nd equation
sin r2sin 90=12
sinr2=12
r2=45

By using 1st equation:
r1=6045=15

sin θsin 15=21 ..(using 3rd equation)
sin θ=21 × sin15
θ=sin1( 2× sin15)

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