Question

A light ray is incident on air liquid interface at 45 degrees and is reflected at 30 degrees what is the refractive index of the liquid? For what angle of incidence will the angle between reflected ray and refracted ray by 90 degrees ​

Answer 1

Given:

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°

Answer 2

Answer:

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