59. The angle of a prism is ’ A ’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2 A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ, of the prism is :

59. The angle of a prism is ’ A ’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2 A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ, of the prism is :

(a) \(2\sin A\)

(b) \(2\cos A\)

(c) \(\tfrac12\cos A\)

(d) \(\tan A\)

Answer :  (b) \(2\cos A\)

\(\frac{\sin i}{\sin r} = \mu\)

\(\frac{\sin 2A}{\sin A} = \mu\)

\(\frac{2 \sin A \cos A}{\sin A} = \mu\)

\(2 \cos A = \mu\)