Q.Why are multiple colours observed over a thin film of oil floating on water? Explain with the help of a diagram.

[!TLDR] Oil-film colours come from division-of-amplitude interference: one ray reflects off the film's top surface, another reflects off its bottom after refracting through, and their path difference (hence which colour interferes constructively) depends on the viewing angle. [!ANSWER] Different colours interfere constructively at different viewing angles because the two interfering rays' path difference within the fil …

A thin oil film floating on water produces its characteristic shimmering colours through DIVISION OF AMPLITUDE interference (Section 7.8.4), a genuinely different mechanism from the division-of-wavefront methods (Young's slits, Lloyd's mirror, biprism) used elsewhere in the chapter. A single incident ray striking the film's top surface splits into two parts: one part reflects immediately off the top surface (ray AE in the diagram), while the rest refracts INTO the film, travels through it to the bottom surface, partially reflects there, and travels back up to refract out again at the top, emerging (ray CF) roughly parallel to and hence able to interfere with the first reflected ray AE. Because ray CF has travelled an EXTRA path through the film (down and back up) compared to ray AE, the two rays arrive with a path (and hence phase) difference that depends on the ANGLE at which the film is being viewed (the angle of incidence at the top surface, $\theta_1$) -- a different viewing angle changes the geometric path length inside the film -- and also depends on the WAVELENGTH of light, since the film's refractive index (which sets the optical path inside it) itself varies slightly with wavelength. Since different wavelengths (colours) satisfy the constructive-interference condition at different viewing angles, the film shows DIFFERENT colours when viewed from different angles -- this is genuinely an interference effect, not the film absorbing or reflecting specific colours via any pigment (a full mathematical treatment must also include t …

Identify thin-film colours as division-of-amplitude interference between a ray reflected at the film's top surface and a ray reflected at its bottom surface (after refracting through), with the two rays' path difference -- and hence which wav …

Attributing the colours to a pigment or dye in the oil itself, rather than recognising them as a genuine interference effect between two reflected rays, whose pa …