Question

A monochromatic ray of light is incident at 37° on an equilateral prism of refractive index 3/2. Determine angle of emergence and angle of deviation. If angle of prism is adjustable, what should its value be for emergent ray to be just possible for the same angle of incidence.

Answer 1

By Snell’s law, in case of prism,

For equilateral prism, A = 60°

Also, A = r₁ + r₂ 

∴ r₂ = A – r₁ = 60° – 23°39′ = 36°21′

Applying snell’s law on the second surface of

= 62°44′ 

≈ 63° 

For any prism,

i + e = A + δ 

∴ δ = (i + e) – A 

= (37 + 63) – 60 

= 40°

For an emergent ray to just emerge, the angle r’₂ acts as a critical angle.

As, A = r’₁ + r’₂ and i to be kept the same.