A light ray in air strikes a glass plate whose index of refraction is 1.42. Some of the light reflects off the surface of the plate, but most of it enters the glass. If the angle of refraction is one-half the angle of reflection, the angle of refraction is closest to which angles?

Given Information:

Index of refraction of glass = n₂ = 1.42

Angle of reflection = θ₁

Angle of refraction in terms of angle of reflection = θ₂ = 0.5θ₁

Required Information:

Angle of refraction = θ₂ = ?

Angle of refraction = θ₂ = 44.76°

Explanation:

We know from the Snell's law that

n₁sinθ₁ = n₂sinθ₂

Where n₁ is index of refraction of air and n₂ is index of refraction of glass, θ₁ is the angle of reflection and θ₂ is the angle of refraction.

Assuming n₁ = 1

1*sinθ₁ = 1.42*sinθ₂

since θ₂ = 0.5θ₁

1*sinθ₁ = 1.42*sin0.5θ₁

1/1.42 = sin0.5θ₁/sinθ₁

sin⁻¹(1/1.42) = sin⁻¹(sin0.5θ₁/sinθ₁)

44.76° = 0.5θ₁

θ₁ = 44.76°/0.5

θ₁ = 89.52°

So the angle of refraction is

θ₂ = 0.5(89.52°)

θ₂ = 44.76°

its a 5.5 n

glad that