## A pattern within a pattern

Diffraction brings light from the two slits together and allows it to interfere.

The single slit patterns merge into one. Dark bands appear inside the bright peaks. By closing a slit we make the dark bands bright! The actual variation of light intensity across the screen (Figure 8.10), is shown underneath the photograph.

We say that the intensity of the interference pattern is 'modulated' by the diffraction pattern.

Figure 8.10 Interference between light from a pair of wider slits.

8.7 Interference as a tool

We may make accurate estimates of length using interferometers. In such instruments a single beam of light is generally split into two beams, which then travel along different paths before being recombined. There is invariably some difference in the lengths of the paths travelled by the individual beams and an interference pattern may be seen. If the path difference changes, even by some fraction of a wavelength, the positions of individual bright and dark bands (fringes) change. The amount of movement is a measure of the change in the path difference.

### 8.7.1 The Michelson interferometer

The Michelson interferometer was developed in 1880 by Albert Michelson (1852-1931) and Edward Morley (1838-1923) in an attempt to measure the speed of the earth through the ether.

The photograph and corresponding sketch of a typical Michelson interferometer may be seen in Figure 8.11.

A beam of light falls on a semi-silvered glass plate (beam splitter) inclined at 45° to the beam. About half of the light is reflected and travels to a plane mirror, M1. The remainder is transmitted and travels to a second plane mirror, M2. The light beams reflected at the two mirrors retrace their paths back to the semi-silvered mirror. Some of the light from M2 is reflected at the back of the semi-silvered mirror and combines with light from M1 transmitted by that mirror.

Figure 8.11 Michelson interferometer.

If the position of the moveable mirror Ml is adjusted, the path difference changes and the fringe pattern expands or contracts. In principle, we can measure the distance the mirror is moved by counting the number of fringes which pass a marker in the field of view. In practice the mirror must be moved in individual steps, each so small that any one particular ring remains in the field of view. After each step, the position of the mirror is adjusted to restore the ring to its original position. In this step-wise manner we can count thousands of fringes.

### A new standard of length

In the 1880s, one metre was defined to be the distance between two fine scratches on a metal bar held in a museum near Paris. Rulers used in laboratories had in principle been calibrated against the standard metre, albeit indirectly and generally many times removed. This procedure with its potential for gross inaccuracy was very unsatisfactory.

Michelson used his interferometer to define the metre in terms of the wavelength of light. The accuracy he achieved was better than 1/100,000 mm. His method was not only much more accurate, but also had the advantage that direct measurements of length could be made in any reasonably equipped laboratory.

Michelson's work paved the way for a new atomic standard of length, which, although used as early as 1925, was not officially implemented until 1960.

The Michelson interferometer may be used to investigate properties of materials. For example, transparent materials may be inserted into one arm of the instrument, or opaque materials such as metals may be polished and substituted for

### Thin film interference

Interference is responsible for the striking displays of colour often given by thin films such as soap bubbles. Light reflected from the upper surface of the film interferes with light reflected from the lower surface to produce interference fringes which generally come in a whole range of colours.

Sound waves stimulate soap films to vibrate. Courtesy of Stefan Huzler, Trinity College, Dublin.

one of the mirrors. 8.8 Thin films

Soap bubble. Courtesy of Mila Zinkova.

The photographs on p. 263 show some spectacular patterns in soap films placed horizontally in a vertical resonance tube*. High frequency (above 850 Hz) sound waves in the tube produce thickness variations as they pass through the films. The images (left and right) were caused by sound waves of two different frequencies. The precise form of the pattern at any one frequency depends on the initial thickness of the film and on the amplitude of the wave. The spacing of adjacent fringes reflects the variations in the thickness of the films.

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