(a) A soap film (n = 1.33) appears bright green (λ = 530 nm) in reflected white light at near-normal incidence. Assuming the thinnest film (m = 0), find t. (b) What colour is transmitted most strongly there? (c) Why does the bubble show a black spot just before bursting? Step 1: Bright in reflection: 2nt = (m + ½)λ. m = 0: t = λ/(4n) = 530/(4×1.33) = 530/5.32 ≈ 99.6 nm ≈ 100 nm. Remarkably thin — about 1/5 of the wavelength! Step 2: Transmitted light: the two transmitted beams have no relative phase flip, so bright transmission needs 2nt = mλ. At t = 100 nm, 2nt = 266 nm — no visible λ satisfies mλ = 266 nm for m ≥ 1 (266 nm is UV). So green is suppressed in transmission; the transmitted colour is white-minus-green = magenta-ish (complementary). Step 3: As t → 0, 2nt → 0 satisfies the destructive condition 2nt = mλ (m = 0) for every λ — all colours cancel in reflection: the black spot. It signals the film is below ~10 nm thick, moments from rupture.