Y and Z are two partially reflecting glass sheets, a distance l apart in air. White light falls normally on Y. The light emerging from Z is analysed by a spectrometer. A dark band is observed in the spectrometer at a wavelength. The distance l must be equal to:

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This question was previously asked in

AAI ATC Junior Executive 2015 Official Paper (Shift 2)

Answer 1

At wavelength λ, a dark fringe will be observed in a spectrometer if destructive interference takes place for that wavelength.

In the case of transmitted light, the path difference is given by Δ = 2 μl cos r

Since light rays are incident normally:

r = 0 and cos r = 1

Hence, the path difference is equal to 2 μl

But for air μ = 1.

Since destructive interference takes place, therefore, the path difference must be equal to an ‘odd multiple of .

Therefore,

Where, n = 0, 1, 2, …