by changing the location of the adjustable mirror. The compensating plate ensures that both beams pass through the same amount of glass,

which is important since light slows down in glass.

The purpose of this equipment is to control and detect with extreme precision changes in the path length difference between the two beams of

light. Michelson knew the relationship between path length differences and interference patterns. A path difference of half a wavelength would

cause the beams to interfere destructively, and a path length difference of an entire wavelength would cause complete constructive

interference.

To measure a tiny increment of path length, Michelson could place a bright fringe at the center of the image created in the viewing telescope by

setting the distance of the adjustable mirror. When he then moved the adjusting mirror a very small distance using a finely threaded screw

adjustment, the image in the telescope would shift so that a dark fringe would be at the center. He knew he had moved the mirror one-quarter

wavelength because the light traveled that additional distance to the adjusting mirror and then traveled back, making for one-half wavelength

difference in total. A half wavelength path difference is the difference between complete constructive and complete destructive interference. In

actual practice, Michelson’s experiment had a few more “tricks” to it than we have described here, but this section conceptually summarizes

how it worked.

34.4 - Thin-film interference

Thin-film interference: The

interference caused by light

waves reflecting off the two

different surfaces of a thin

film.

In soap bubbles and in thin layers of gasoline or oil

floating on water, you sometimes see “rainbows,” light

of all the colors of the spectrum. The causes of

rainbows in the sky and rainbows in soap bubbles are

quite different. Those celestial “Pot-of-gold” rainbows are caused by refraction and

reflection. Soap-bubble rainbows are caused by a phenomenon called thin-film

interference.

To understand thin-film interference, we start with the fact that when light reflects off a

material with a higher index of refraction than the medium it is traveling in, it changes

phase by 180°. When it reflects off a material with a lower index of refraction than the

medium it is traveling in, there is no phase change.

Specifically, when light reaches the front surface of a thin film surrounded by air, some

of it reflects, and changes phase by 180°. Some of the light passes through this first

surface, and then reflects off the far surface of the film. No phase change occurs here.

As the light moves between the two media, it refracts as well.

This combination of reflection and refraction is illustrated in Concept 1. You see a

downward ray striking the film from the upper left. Some of it reflects when it reaches

the film’s top surface, and we call that reflected ray 1. Some of the light passes into the

film, reflects at the bottom surface, and passes back through the film again. We call that

ray 2.

The initial ray of light becomes two rays that have a somewhat complicated relationship in terms of their phase difference. Ray 1 changes

phase 180° as it reflects, and ray 2 does not change phase as it reflects but it travels an extra distance through the film that ray 1 does not.

Depending on the path length difference, which equals roughly twice the thickness of the film, the two rays could end up completely in phase,

completely out of phase, or somewhere in between.

Interference depends not just on path difference but on wavelength as well. The type of interference occurring at a specific point in a thin film

will differ by the local thickness of the film and the wavelength, or color, of the light. White light has components consisting of many colors, and

in a film of variable thickness these components will interfere differently at different points.

What about the rainbow of colors you can observe on a soap bubble or oil sheen? The film of a soap bubble can be thicker or thinner at various

locations. The path length difference at a certain point on a soap bubble may cause destructive interference for red light, but constructive

interference for blue light. This means you perceive this region as blue. At another point, the bubble will have a different thickness, and the path

length difference may cause the opposite result, and you see red there. These patterns can change quickly. A slight breeze or the flow of soap

to the bottom of the bubble will cause parts of it to change thickness, resulting in a new pattern.

A region of a bubble that is about to burst is often thin enough that all wavelengths of light destructively interfere there, and the bubble appears

dark. The path length difference through this part of the film is essentially zero, so the change of phase accompanying reflection at the front

surface, which affects all wavelengths equally, causes destructive interference.

Thin-film interference in soap bubbles.

Thin-film interference

Interference “rainbow” caused by:

·change of phase on first reflection

·difference in travel distance of rays

·variations in thickness of film

(^630) Copyright 2000-2007 Kinetic Books Co. Chapter 34