Question

How is the critical angle related to the refractive index of a medium?

Answer 1

The relationship is `""_amu_m = 1/sin C`

When a light beam enters a liquid (m) from point A, it becomes ∠i = C with normal and emerges from the liquid in medium air, which is rarer, producing ∠r = 90°, or the ray BO becoming parallel to the liquid surface.

∴ `""_mmu_a = sin i/sin r = sin C/(sin 90°)`

Or `""_amu_m = (sin 90°)/sin C = 1/sin C`

∴ `""_amu_m = "R.I of medium" = 1/sin C`