Question

A ray in air is incident on a glass plate whose index of refraction is 1.40. The angle of refraction is one-half the angle of reflection. The angle of refraction is closest to

Answer 1

46⁰

Step-by-step explanation:

We solve this by using snell's law

n1sinθ1 = nrSinθr

n1 and nr = refractive index of incident medium and also refractive medium

We have that θ1 = θr/2

Such that

1 sin2θr = 1.40Sinθr

Sin2θ = 2sinθcosθ when we use trigonometric identity

2sinθrCosθr = 1.40sinθr

Cosθr = 1.40/2

= 0.7

θr = cos^-1(0.7)

= 45.57⁰

This is approximately 46⁰