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Thin Film Interference
Wedge Shaped Films
If two flat pieces of glass are held at a very small angle to each other and viewed under a microscope (as shown below), a regular series of bright and dark lines can be observed.
These lines are interference fringes.
If the microscope is a travelling microscope*, the distance between these interference fringes can be measured.

The interference is between light reflected from the lower surface of the top piece of glass (an internal reflection) and the upper surface of the bottom piece of glass (an external reflection).
The path difference is therefore twice the thickness of the space between the pieces of glass at that position  (2s1 or 2s2 referring to the diagram below).

At an external reflection a phase change of π rad occurs.
At an internal reflection there is no phase change.
Therefore, if the path difference is equal to a whole number of wavelengths, destructive interference will occur and a dark fringe will be seen.
If the path difference is an odd number of half wavelengths, a bright fringe will be seen.

In the next diagram, the numbers 0 to 10 represent the positions of 11 consecutive dark fringes.

Moving from one dark fringe to the next, corresponds to a change in the path difference of one wavelength, λ.
This corresponds to a change in the thickness of the film of λ/2.
Therefore, the total change in thickness, y, is equal to 5λ.

Looking at the diagram, we see that
so, in this case, (working on 11 fringes) we have
If the distance, x is measured using the travelling microscope and the wavelength of the light being used is known, the angle, θ, of the wedge can be calculated.
This gives us a possible way of measuring the size of very small objects, for example, the thickness of a hair.
The hair is used to separate the two pieces of glass and measurements of the interference fringes are made.
If greater precision is needed, just measure the distance between a larger number of fringes.

*No, not a microscope you take with you on holiday; a microscope which is fixed to a movable support. Changes in the position of the microscope can be measured (often using a Vernier scale).

Parallel Sided Films
The colours seen in soap bubbles are due to between light reflected from the two surfaces of the bubble.
A similar interference effect occurs in thin layers of oil on water.

A practical use of this kind of interference is found in the coating of high quality lenses for cameras, telescopes etc.
When light enters a lens some of it is reflected from the lens surface.

The intensity of the light entering the optical instrument is reduced by this reflection.
The next diagram shows a magnified view of the front surface of a coated (or “bloomed”) lens in which two reflections occur.

Both these reflections are external reflections as light going from less to a more dense medium.
This means that a phase change of πrads occurs in both cases.
Therefore, if the thickness of the film is equal to one quarter of a wavelength, the two reflections will interfere destructively.
The destructive interference means that the net amount of light reflected is reduced and the amount of light transmitted into the instruments is greater than without the thin film.
This might sound paradoxical and a (slightly) more satisfying explanation can be found using the particle model of light.
However, it works: a “bloomed” lens transmits more light than one with no coating!
Note that the thickness of the film can only be exactly right for a given wavelength.
However, in practice a range of wavelengths are affected.
In most cases the thickness is chosen to give cancellation of the reflections near the middle of the visible spectrum.
This is why lens surfaces often appear to be purple when viewed under reflected white light; the reflections of the other colours are greatly reduced.

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