# Why oil films still have color when illuminated by an incoherent source (sun) at oblique incidence

I understand how coherent light can produce interference patterns with a thin oil film. However the sun is a spatially incoherent light source.

How can it be that at oblique incidence I still see colors caused by inteference. Because when at an angle, the rays that interfere come from different spatial positions of the sun. At normal incidence the light ray would interfere with itself and the interference effects depend on the temporal coherence.

I don't think I can use the Van Cittert-Zernike theorem here because I am considering two parallel rays which do not originate at the same point (Or can I assume this, because the sun is so far away?).

The destructive interference happens for certain small region of the spectrum (i.e. the part of the spectrum such that the optical path length difference is half the wavelength). It's true that temporal coherence of broadband source is short, and we associate short temporal coherence with short coherence length: if the optical path length difference is longer than the coherence length, the interference pattern averages out. However, even when the optical path length is longer than the coherence length, you do expect some spectral density within your light to achieve thin-film interference condition, and that part of the spectrum will appear dim due to destructive interference.

If you shine a narrowband light instead of broadband, you won't see color changes but more like bright-and-dark fringes.

And regarding spatial coherence, yes, if the sunlight were to have a terrible spatial coherence (huge wavefront aberration across a small patch of the film), the color pattern will be likely ruined, but I think sunlight decently approximates a spatially coherent source (it's not a point source but close).

IMO your picture is wrong. Interference doesn't take place between waves originated from different Sun's places but for just one wave reaching different points of oil film.

So you have an infinity of interference patterns, one for each point of the extended source (the Sun). If these patterns had an angular fringe separation smaller than Sun's angular size, you wouldn't see no fringes. But this doesn't happen.

Note that an analogous issue arises with rainbow (which isn't an interference phenomenon). Each point of Sun causes its own rainbow and they superpose producing a smeared rainbow. Happily the angular extension of rainbow (about $$2.8^\circ$$) is greater than Sun's angular size ($$0.5^\circ$$) - otherwise we wouldn't know of that beautiful sight.

• So basically what you are saying is that I can use the van Cittert-Zernike theorem to calculate the mutual coherence. Because the angular size of the sun is small enough? Apr 27 '19 at 10:08
• @tgoossens, the van Cittert-Zernike theorem relates to quasi-monochromatic light, but the Sunlight is clearly a broadband light. Why do you think the theorem is relevant to the problem?
– wcc
Apr 28 '19 at 0:47

The interference explanation is an excellent classical one but a photon is never destroyed by photons cancelling each other. The photon "wave function" helps to explain that certain wavelengths cannot traverse a thin film due to its non-ideal path length, the colours are visible as some wavelengths are transmitted and others reflected. I.e. a thin film does work for a single photons.

• " I.e. a thin film does work for a single photons." Also at oblique incidence then? Apr 27 '19 at 9:45
• Yes but bear in mind that the path length thru the film also changes with angle. When a dichroic filter is made (see Thor labs) to reflect or transmit a certain color band (or bands) many thin layers are put down (100s) so that the angular performance is improved. Apr 27 '19 at 15:28