Doublet Separation, Experiment

The experimental procedure involves examining the interference fringes of the light at normal incidence ( angle = 0°) such that constructive interference is produced by one wavelength of the doublet

while the other wavelength is adjusted to a half-integer condition. This can be seen in the interference pattern as a weaker ring half-way between the stronger interference maxima. This corresponds to

Advancing the micrometer until this condition occurs again provides data from which the doublet separation can be calculated.

Subraction of the two distances obtained in the doublet experiment gives the following expression:

This expresses the fact that the shorter wavelength has gained an order on the longer wavelength. Combining terms gives

Substituting this back into the top equation gives

The relationship for the doublet separation is then

Calculation

Doublet Separation, Fabry-Perot

The resolvance of the Fabry-Perot interferometer is sufficient to resolve closely spaced spectral doublets like the sodium doublet and the hydrogen-deuterium doublet.

The experimental procedure yields a distance of movement of the interferometer mirror which allows the doublet separation to be calculated from the relationship

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The average wavelength of the doublet must be known from other measurements to make use of this relationship.

The default values in the calculation are for the sodium doublet. You may change the numbers to explore variations.