Practice question

**Prism formula** for small A, δ_m≈(n-1)A, for 30°, n=1.6, δ_m≈0.6×30°=18°, approximate, exact using sin formula. For 45°, n=1.6, sin[(45+δ_m)/2]=1.6×sin22.5°=1.6×0.3827=0.6123, (45+δ_m)/2=37.8°, δ_m=30.6°, showing deviation increases with A and n. Snell’s law: n₁ sin i = n₂ sin r . Glass ( n₁ = 1.5 ), water ( n₂ = 1.33 ), i = 30° . 1.5 × sin 30° = 1.33 × sin r . sin 30° = 0.5 ⇒ 1.5 × 0.5 = 1.33 sin r ⇒ 0.75 = 1.33 sin r . sin r = (0.75/1.33) ≈ 0.564 ⇒ r = sin⁻¹(0.564) ≈ 34.3° . Substituting values gives 34°, which matches expected image position