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Thermodynamics

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Visibility of Fringes

In the case of Michelson interferometer, the intensity is given by

d is the distance between M₁ and M₂’. The intensity is maximum when δ is an integral multiple of 2π. The intensity is zero when δ is an odd multiple of π. When a monochromatic source of light is used, the minimum intensity of the fringes is zero. The visibility of fringes in the case of a Michelson interferometer is

For monochromatic light,

I_min = 0

∴ V = 1

However, if the source of light is not strictly monochromatic, but contains two nearby wavelengths, the condition for maximum intensity for both the wavelengths is satisfied only for particular values of path difference (2d cos θ).

As the value of d is altered, the two wavelengths do coincide over a considerable range and here the fringe visibility is maximum. For values of d other than maximum intensity positions for both the wavelengths, the two fringe patterns will be complimentary and the minimum visibility will be zero, provided the intensities for both the wavelengths are equal. If intensities are not equal, the minimum visibility will not be zero. The minimum visibility will be

Here a₁ and a₂ are the amplitudes.

Hence the source will be perfectly monochromatic if visibility is maximum and constant for different values of 2d cos θ. If the visibility changes with the change of 2d cos θ, the source is not strictly monochromatic.