Question

a light ray is incident on air-liquid interface at 45° and is refracted at 30° . what is the refractive index of the liquid? for what angle of incidecnce will the angle between reflected ray refracted ray be 90°

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

Guy's ur answer is

The Angles of incidence I = 54.7 degrees

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