A prism has apex angle A = 60°. In the minimum-deviation position, the deviation is δ_m = 38°. (a) Find the refractive index. (b) Find the incidence angle at minimum deviation. (c) For a thin prism of A = 4° made of the same glass, estimate δ. Step 1: n = sin((A + δ_m)/2)/sin(A/2) = sin((60 + 38)/2)/sin30° = sin49°/0.5 = 0.7547/0.5 ≈ 1.509. (Typical crown glass ✓.) Step 2: At minimum deviation i = (A + δ_m)/2 = 49°. Check: r₁ = A/2 = 30°, Snell: sin i = n sin r₁ → sin49° = 0.7547; 1.509 × sin30° = 0.7545 ✓. Step 3: Thin prism: δ ≈ (n − 1)A = 0.509 × 4° ≈ 2.04°. The thin-prism formula is why weak "prism" corrections in spectacles are prescribed directly in dioptres of deviation.