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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.
If the microscope is a travelling microscope, the distance between these interference fringes can be measured with reasonable precision.
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 (s1 or s2 in the diagram below) is therefore twice the thickness of the space between the pieces of glass at that position.
Diagrams not to scale.
At an external reflection there is a phase change of rad so if the path difference, s, is equal to n, 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 diagram above, 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, . This corresponds to a change in the thickness of the film of /2.
Therefore, the total change in thickness, y, is equal to 5.
If the distance, x is measured using the travelling microscope and the wavelength of the light being used is known, the angle, q, 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.