devarshi-dt-logo

Question:

Let the x-y plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a 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√3 î→ + 8√3 ĵ→ + 10 k→ is incident on the plane of separation. The angle of refraction in medium 2 is?

30°

60°

45°

75°

Solution:

Angle of incidence with Z direction (normal)
cosα = 10/√((6√3)² + (8√3)² + (10)²) = ½
α = 60°.
So, μ₁ sinα = μ₂ sinβ
√2 × sin 60 = √3 sinβ
β = 45°