Question

A ray of light is incident at grazing incidence on one face of an equilateral prism made from a transparent material of refractive index √2 . The angle of emergence, and the angle of deviation, for this ray, would be equal to (respectively),

(1) sin^-1 [√2 sin15°] and {π/6 + sin^-1 [√2 sin 15°]}

(2) sin^-1 [√2 sin75°] and {π/6 + sin^-1 [√2 sin 15°]}

(3) sin^-1 [√2 sin75°] and {π/6 + sin^-1 [√2 cos 15°]}

(4) sin^-1 [√2 sin15°] and {π/6 + sin^-1 [√2 cos 15°]}

Answer 1

(1) sin^-1 [√2 sin15°] and {π/6 + sin^-1 [√2 sin 15°]}

For the ray, incident at grazing incidence, on one face, the corresponding angle of refraction, r₁ , would be given by 

If angle of incidence, at the second face, is r₂ , we would have

∴ If e is the angle of emergence, we have

Also, if D is the angle of deviation, we have