Colours of Thin Films

A drop of oil on a wet road, a soap bubble, the wing of a dragonfly: all shimmer with colours that shift as you tilt your head. None of them contain any dye. The colours come from interference.

Many reflections#

Take a thin transparent film of thickness d and refractive index μ, with parallel faces. Light falling on it splits at the top face: part reflects, part enters. The part inside splits again at the bottom face: part leaves, part reflects back up, and so on. The film sends out a whole series of reflected waves and a series of transmitted waves, each weaker than the last. The film can be viewed by either set.

Take nearly normal incidence. Each transmitted wave has made one more round trip inside the film than the one before: an extra geometrical path 2d, through a medium of index μ. So neighbouring waves differ in optical path by

Seen by transmitted light#

Seen by reflected light: a twist#

You might expect the same conditions for reflected light. But think about energy: if a film both transmitted and reflected a wavelength strongly, where would the extra energy come from? Whatever the film transmits strongly it must reflect weakly, and vice versa. Experiment confirms that the conditions swap:

The reason: a phase flip on reflection

Recall a pulse on a light string running into a heavier one: the reflected pulse is inverted, a phase change of π. Reflected from a lighter string, it isn’t. Light behaves the same way: a medium of higher refractive index is optically denser.

So even when 2μd is a whole number of wavelengths, the first two reflected waves end up half a cycle apart and cancel.

Where the colours come from#

In white light, a given thickness satisfies the bright condition for some wavelengths and the dark condition for others. Those colours are reflected strongly or weakly, and the eye sees the mixture. Where the thickness varies, as in a draining soap film or a spreading oil slick, the colours vary in bands. A film much thinner than a wavelength reflects almost nothing (2μd ≈ 0, so the reflection is dark): the top of a soap film turns black just before it bursts.