A light ray is incident on air-liquid interface at 45^o and is refracted at 30°. What is the refractive index of the liquid? For what at angle of incidence will the angle between reflected ray and reflected ray be 90^o? (AS7)

Given;

Angle of incidence i = 45°
Angle of refraction r = 30°
Refractive index = n =

⇒ n =

⇒ n = = 1.141.

Refractive index of liquid = 1.414

Given;

The angle between the reflected and refracted ray = 90°
⇒ angle of reflection (r) + angle of incidence (i) = 90°

⇒ Angle of refraction (r) = (90° - i)
But refractive index n =

⇒ n =

⇒ n = tan i

⇒1.414 = tan(i);

From Natural tangent tables tan 54.7° = 1.414 = tan i
The angle of incidence i = 54.7°