Thin Film Interference

Light reflects from both the top and bottom surfaces of a thin film, producing interference between the two reflected beams.

Path difference between the two reflected rays: 2nt cos θ_t, where n = film index, t = film thickness, θ_t = angle inside the film.

When reflection occurs at a denser medium, the reflected wave undergoes a π phase shift (equivalent to extra λ/2 path).

Soap film in air (n_film > n_air, single denser-medium reflection at top): bright when 2nt cos θ_t = (m + ½)λ.

Anti-reflection coating on glass: film of index √n_glass, thickness λ/(4n_film) — destructive interference suppresses reflection at one wavelength.

The vivid colours of soap bubbles, oil slicks, and butterfly wings come from selective wavelength interference — thickness varies, so different colours appear at different places.

Newton's rings: a special thin-film geometry (plano-convex lens on flat glass) — concentric dark/bright rings centered on contact point.