Practice question

**Critical angle** C satisfies sinC = n₂/n₁, n₁>n₂, n₂=1 for air, n₁=1.52 for glass gives sinC=1/1.52=0.6579, C≈41.1°, for water n=1.33 C=48.75°. Beyond C, total internal reflection occurs, all light reflected, no refracted ray, used in optical fibers and prisms. Snell’s law: n₁ sin i = n₂ sin r . 1.33 sin 30° = 1.5 sin r . sin 30° = 0.5 ⇒ 1.33 × 0.5 = 1.5 sin r ⇒ 0.665 = 1.5 sin r . sin r = (0.665/1.5) ≈ 0.443 ⇒ r = sin⁻¹(0.443) ≈ 26.3° . Substituting values gives 26°, which matches expected image position and magnification from mirror/lens formula 1/f =