Question

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

(A) tan A 

(B) 2 sin A 

(C) 2 cos A 

(D) cos (A/2)

Answer 1

The correct option is (C) 2 cos A.

Explanation:

In order to retrace its path, the ray must fall on silvered surface at an angle of 90°. 

∴ in ΔADE, A + 90 + ∠D = 180° 

∴ ∠D = 90 – Å 

∴ also r + ∠D = 90° 

∴ r = Å 

As Refractive index = [(sin i) / (sin r)] 

Hence n = [(sin2A) / (sinA)] = [(2sinAcosA) / (sinA)] 

∴ n = 2cosA