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

Options

A. `2 sin A`
B. `2 cos A`
C. `(1)/(2) cos A`
D. `tan A`

Answer

B

Explanation

As the refracted from first surface of prism returns back through the same path, it must be falling on the silvered surface at `90^@`, as shown in Fig.
`:. r = 90^@ - (90^@ - A) = A`, when
`i = 2 A`
`mu = (sin i)/(sin r) = (sin 2 A)/(sin A) = (2 sin A cos A)/(sin A) = 2 cos A`.
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