Question

A light ray enters into a liquid at an angle 45 degrees and gets refracted at an abgle of 30 degrees with respect to normal. Calculate refractive index of the fluid. (sin 45 degree= 0.7 and sin 30 degree= 0.5)

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=1.414
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°