(a) Derive Snell's law numerically: a wavefront in air (v₁ = c) meets water (v₂ = 0.75c). In time t the free edge travels BC = 3.0 cm in air. What is the wavelet radius in water, and if AC = 6.0 cm, find i and r and verify Snell's law. (b) At what incidence does the refracted envelope vanish for water→air? Step 1: AE = v₂t = 0.75 × BC = 2.25 cm. sin i = BC/AC = 3.0/6.0 = 0.5 → i = 30°. sin r = AE/AC = 2.25/6.0 = 0.375 → r ≈ 22.0°. Step 2: Check: sin i/sin r = 0.5/0.375 = 1.333 = v₁/v₂ = c/0.75c ✓ = n_water. The wavelet radii (3.0 vs 2.25 cm) visibly encode the speed ratio. Step 3: Water→air: need sin r = (v_air/v_water) sin i = 1.333 sin i ≤ 1 → sin i ≤ 0.75 → i_c ≈ 48.6°. Beyond this the envelope construction fails — total internal reflection, derived purely from wavelet geometry.