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Q.

Angle of a prism is A and its one surface is silvered. Light rays falling at an angle of incidence of 2A on the first surface return back through the same path after suffering reflection at the second silvered surface. Refractive index of the material of prism is

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a

2sinA

b

2cosA

c

1/2cosA

d

tanA

answer is B.

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Detailed Solution

To retrace its path light rays should fall normally on the reflecting surface. So
$\begin{array}{l} r_{2} = 0 \\ \Rightarrow r_{1} = A - r_{2} \Rightarrow r_{1} = A \end{array}$
Now applying Snell's rule between incident ray and refracted ray.
(1)sin(2A)=nsin(A)

$\Rightarrow 2 \sin A \cos A = n \sin A \Rightarrow n = 2 \cos A$

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