A ray in air is incident on a glass plate whose index of refraction is 1.53. The angle of refraction is one-half the angle of reflection. The angle of refraction ( in degree) is closest to:

Answer 1

Use Snell's Law.

n₁sin(θ₁) = n₂sin(θ₂)

Since medium 1 is air, n₁ = 1, and it is given that n₂ = 1.53. It is also given that θ₂ = θ₁/2. So we have the following.

sin(θ₁) = 1.53sin(θ₁/2)

Here's the trick: Use the Double Angle Formula for the sine function on the left side.

2sin(θ₁/2)cos(θ₁/2) = 1.53sin(θ₁/2)

Cancel the factor of sin(θ₁/2) on both sides.

2cos(θ₁/2) = 1.53

cos(θ₁/2) = 1.53/2 = 0.765

θ₁/2 = cos^-1(0.765) = 40.1^ο

θ₁ = 80.2^ο