• Tags: thin-film, interference, colors
• Difficulty: Moderate

When light reflects from a thin film of thickness t and refractive index μ, interference occurs between rays reflected from the top and bottom surfaces. For near-normal incidence:

Path difference = 2μt (geometric) + λ/2 (phase change at reflection from denser medium).

Constructive (bright): 2μt = (2n-1)λ/2 (accounting for the extra λ/2 from reflection). Destructive (dark): 2μt = nλ.

If both reflections are from denser-to-rarer or both rarer-to-denser interfaces, there is no net phase change and the conditions swap. Colors in soap bubbles and oil films arise from constructive interference of specific wavelengths depending on the local thickness.