15.6 Interference in Thin Films
We often see bright bands of color when light reflects from a thin layer of oil floating on water or from a soap bubble. These are the results of interference. Light waves are reflected from the front and back surfaces of such thin films, and constructive interference between the two reflected waves (with different path lengths) occurs in different places for different wavelengths. Fig. 15.11 shows the situation. Light shining on the upper surface of a thin film with thickness is partly reflected at the upper surface (path abc) of thin film. Light transmitted through the upper surface is partly reflected at the lower surface (path abdef). The two reflected waves come together at point P on the retina of the eye. Depending on the phase relationship, they may interfere constructively or destructively. Different colors have different wavelengths, so the interference may be constructive for some colors and destructive for others.
(Fig. 15.11: Thin Film)
That's why we see coloured patterns in thin film as in Fig. 15.12 (which shows thin films of soap solution that make up the bubble walls). In similar fashion, thin film of floating on water shows same pattern. The complex shapes of the colored patterns result from variations in the thickness of the film.
(Fig. 15.12: White light falling on soap bubble)
Let's look at a simplified situation in which monochromatic light reflects from two nearly parallel surfaces at nearly normal incidence. Fig 15.13 shows two plates of glass separated by a thin wedge, or film, of air. We want to consider interference between the two light waves reflected from the surfaces adjacent to the air wedge. (Reflections also occur at the top surface of the upper plate and the bottom surface of the lower plate; to keep our discussion simple, we won't include these.) The situation is the same as in Fig. 15.13(a) except that the film (wedge) thickness is not uniform. The path difference between the two waves is just twice the thickness of the air wedge at each point. At points where is an integer number of wave lengths, we expect to see constructive interference and a bright area; where it is a half-integer number of wavelengths, we expect to see destructive interference and a dark area. Where the plates are in contact, there is practically no path difference, and we expect a bright area.
(Fig. 15.13: Thin film)
When we carry out the experiment, the bright and dark fringes appear, but they are interchanged! Along the line where the plates are in contact, we find a dark fringe, not a bright one. This suggests that one or the other of the reflected waves has undergone a half cycle phase shift during its reflection. In that case the two waves that are reflected at the line of contact are a half-cycle out of phase even though they have the same path length.
In fact, this phase shift can be predicted from Maxwell's equations and the electromagnetic nature of light.