Question

a light ray is incident on air liquid interface at 45 degree and is refracted at 30 degree. what is the refractive index of the liquid ​

Answer 1

Angle of incidence i = 45°

Angle of refraction r = 30°

refractive index =n=sin i /sin r

=sin45°/sin 30°

=1/√2/1/2⇒2/√2⇒√2=1.4.14

Given the angle between the reflected and refracted ray = 90°

It means angle of reflection (r) + angle of incidence (i) = 90°

Angle of refraction (r) = (90° - i)

But refractive index n = sin i/ sin r

=sin i/ sin(90-i)

=sin i/ cos i (∵sin(90-θ)=cos θ)

From Natural tangent tables tan 54.7° = 1.414 = tan i

The angle of incidence i = 54.7°