Let the x - z plane be the boundary between two transparent media

• Optics

Let the x - z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has refractive index of √2 and medium 2 with z < 0 has a refractive index of √3. A ray of light in medium 1 given by the vector A = 6√3i + 8√3j - 10k in incident on the plane of separation. The angle of refraction in medium 2 is

1. 75°
2. 60°
3. 45°
4. 30°

Answer

μ₁ sinθ₁ = μ₂ sinθ₂ 

cosθ₁ = 1/2

θ₁ = 60°

√2 sin60° = √3 sinθ₂

√(2 x 3)/2 = √3 sinθ₂

sinθ₂ = 1/√2

θ₂ = 45°

The correct option is C.