Practice question

**Prism minimum deviation** δ_m satisfies n = sin[(A+δ_m)/2]/sin(A/2), A prism angle (degrees), n refractive index, δ_m minimum deviation. For A=60°, n=1.45, sin[(60+δ_m)/2]=1.45×sin30°=0.725, (60+δ_m)/2=46.5°, 60+δ_m=93°, δ_m=33°, illustrating n increase raises δ_m. Snell’s law: n₁ sin i = n₂ sin r . Water ( n₁ = 1.33 ), glass ( n₂ = 1.62 ), i = 45° . 1.33 × sin 45° = 1.62 × sin r . sin 45° = 0.707 ⇒ 1.33 × 0.707 = 1.62 sin r ⇒ 0.941 = 1.62 sin r . sin r = (0.941/1.62) ≈ 0.581 ⇒ r = sin⁻¹(0.581) ≈ 35.5° . Substituting values gives 36°, which matches expected