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>> $The refractive index of the material of$

Question

The refractive index of the material of a prism is $2$ and the angle of the prism is $3 0^{o}$ . One of the two refracting surface of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is?

A

$3 0^{o}$

B

$6 0^{o}$

C

Zero

D

$4 5^{o}$

Medium

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Solution

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Correct option is D)

Using $A = r_{1} + r_{2}$

$30 = r_{1} + 0$

so $r_{1} = 30$

Using Snell's Law, $1 \times s i n i = μ \times s i n r$

$1 \times s i n i = 2 \times s i n 30 = 23 / 2$

$s i n i = 1 / 2$

$i = 4 5^{o}$

option 4 is correct

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