# Thin-Film interference confusion

While studying thin-film interference on wikipedia, I encountered a problem. The picture in the link shows a colorful pattern formed on the oil film, that is, the oil film also acts as a screen on which the interfered light reflects and then enters our eye.

But the diagram for the derivation of the mathematical expression shows that the interference of reflected and transmitted light occurs somewhere above the oil film, that is, the screen is somewhere beyond the film, in air. I cannot understand that. (Derivation Image Link)

I think the third diagram is a correct way of explaining the colorful pattern because the upper surface of the film acts as a screen for the interfered light which also reflects the interfered light to our eyes so that we can observe the pattern.(Diagram image link)

Can anyone clarify?

## 1 Answer

The diagram is a bit misleading. They have drawn a single incident ray that is partially reflected and partially transmitted at point A. The transmitted ray emerges from the glass at point C. A dotted line is drawn from point C on the transmitted ray to point D on the reflected ray.

To make the diagram complete, a second incident ray should be drawn parallel to the first incident ray,, striking the glass at point E, a distance AC to the left of point A.. That second incident ray will be partially reflected and partially transmitted like the first incident ray. Along line AD (and beyond) the reflected beam from the first incident ray will overlap with the transmitted ray from the second incident ray. Because they specify that optical path ABC is a multiple of the wavelength, the new incident ray will be that same amount ABC longer than the first ray when they both reach point D.

Interference occurs wherever the incident rays overlap.

• The two parallel rays in the Wikipedia diagram will come to a focus on your retina (or on a screen if a lens is used) and will interfere. So the diagram does illustrate interference as usually considered. Commented Jan 1, 2020 at 14:40
• That's true, if the eye is included in the diagram- but I didn't see an eye there or in the description. Commented Jan 1, 2020 at 14:45
• In order to understand the pattern in the first image, the last diagram (en.wikipedia.org/wiki/File:Thin_film_interference_phase_1.svg) makes much more sense as it shows two incident rays instead of one (as @S. McGrew also said). It shows both the rays interfering at the upper surface of the film and the interfered light then moving away from the surface (to our eyes at C, if they had drawn one). Commented Jan 2, 2020 at 9:12
• Two separate incident rays will not be coherent unless coming from a point source. That's why the first diagram OP references is more generally used - a single ray is broken up into reflected and refracted rays which will remain more or less coherent if the film thickness is not too large. Commented Jan 2, 2020 at 14:43
• That's true, except in that case the refracted and reflected rays won't overlap in the region right above the glass; and I suspect that the single-ray illustration is what (rightly) seemed confusing to the OP. Commented Jan 2, 2020 at 15:03