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The “sodium doublet” is a well-known pair of spectral emission lines at 589.592 nm and 588.995...

The “sodium doublet” is a well-known pair of spectral emission lines at 589.592 nm and 588.995 nm, which appears in the spectrum of the Sun as well as other stars. If we build a spectrograph consisting of grooves separated by 1.00 µm,

a) What is the angular separation between the first-order maxima for the two lines?

b) How far away must the plane of the detector be from the grating so that the two lines are 8.00 µm apart on the detector?

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