Question

A ray of light strikes a plane mirror at an angle of incidence 45° as shown in the figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4°. Through what angle must the mirror be rotated if the total deviation of the ray be 90°?

Answer 1

Deviation caused by mirror

δ₁ = 180° - 2i = 180° - 2 x 45° = 90°

Deviation caused by small angled prism

δ₂ = (µ - 1) α = (1.5 - 1) 4° = 2° (always)

Net deviation produced by the system

= δ₁ + δ₂ = 90° + 2° = 92° > 90°

Greater is angle of incidence on mirror, smaller is the deviation.

Let the mirror be rotated clockwise by an angle to increase angle of incidence.

The deviation produced by the mirror

= 180° - 2 (45° + ß) = 90 - 2ß

Total deviation produced = 90 - 2ß + 2° = 92° - 2ß

∴ given 92°- 2ß = 90°

or ß = 1°