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Draw a schematic diagram of a Michelson interferometer. Describe a setup that allows a pattern of circular interference fringes, localised at infinity, to be observed.

For monochromatic light, derive an expression for the intensity of the interference fringes as a function of the angle θ of observation to the optical axis of the instrument, and D, the difference in the path-length on the optical axis between the two arms of the interferometer.

Such an interferometer is illuminated by light from a sodium lamp, which emits two narrow spectral lines at wavelengths of 589.0 nm and 589.6 nm, with the intensity of the 589.0 nm line being twice that of the 589.6 nm line. Show that there are values of d at which the visibility of the interference pattern has minima, and calculate the smallest value on the optical axis, where θ = 0.

The sodium lamp is replaced by a lamp that emits a single broad line at a similar wavelength, whose spectral linewidth is about 0.6 nm, and an interferogram is recorded by moving one of the mirrors of the interferometer. Describe qualitatively how the intensity as a function of d differs from the case with the sodium lamp, and discuss how far it is necessary to move one of the mirrors in order to distinguish between the two types of illuminating lamp.