Thin Film Example

question: A soap film with index of refraction 1.3 is 450 nm thick. If this film is illuminated with white light perpendicular to the surface of the film, what is the color of the reflected light?

answer: Remember that for n₁< n₂> n₃, t = (m+)$\lambda$/(2n) m = 0, 1, 2, 3, ... for constructive interference (n_air approximately 1).

The only wavelength above that is visible (between 400 and 700 nm) is 468 nm. Thus the film will appear blue when illuminated with white light. Note that this wavelength is the wavelength of the light in air.

Note also that if the film is very thin compared with the wavelength of visible light, no wavelengths will interfere constructively and the film will appear black. You can see this in the middle of a soap film just before it breaks.

question: what would happen if this film were a coating on a glass lens with index of refraction 1.45?

answer: in this case we would have n₁< n₂< n₃ and the situation would be destructive interference for 468 nm. The lens would reflect not reflect light with wave lengths in this region.