The X-Y plane be taken as the boundary between two transparent media M₁ and M₂. M₁ in Z ≥ 0 has a refractive index of √2 and M₂ with Z

Question

The X-Y plane be taken as the boundary between two transparent media M₁ and M₂. M₁ in Z ≥ 0 has a refractive index of √2 and M₂ with Z < 0 has refractive index of √3. A ray of light travelling in M₁ along the direction given by the vector p⃗ = 4√3 î-3√3 ĵ-5k̂, is incident on the plane of separation. The value of difference between the angle of incident in M₁ and the angle of refraction in M₂ will be degree.

Accepted Answer

15. Normal is along k̂. |p⃗| = √48+27+25 = 10. cos i = 5/(10), so i = 60°. √2 sin 60° = √3 sin r gives sin r = 1/(√2), r = 45°. i-r = 15°. → 15

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