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Question

A ray of light is incident at an angle of 45 on a square slab of a transparent material. What should be the refractive index of the material of the slab so that total internal reflection occurs at the vertical face AB?


A

2

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B

32

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C

1.5

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D

53

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Solution

The correct option is B

32


Consider the refractive index of the slab to be x.
Light ray travels from medium 1 to medium 2.
By Snell's law,
sin isin r=Refractive index of medium 2Refractive index of medium 1
At the first interface
sin 45osin r=x1 ..(1)
At the second interface
cos r=1x
sin r=x21x ..(2)
from (1) and (2)
12 × x21x=x
12=x21
x21=12
x2=32
x=32


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