Monochromatic light of wavelength 633 nm from a laser is incident normally on a diffraction grating. The grating has 500 lines per millimeter.
(a) Calculate the angle at which the first-order maximum is observed.
[2]
(b) Determine the maximum number of orders that can be observed with this grating and wavelength.
[3]
(c) The laser light is replaced by a source emitting two closely spaced wavelengths, 589.0 nm and 589.6 nm (sodium doublet). Calculate the angular separation of the first-order maxima for these two wavelengths.
[2]
(d) Outline how increasing the number of lines per millimeter of the grating affects the angular separation calculated in (c).
[1]
Question
Calculate the angle at which the first-order maximum is observed.\n[2]
Hint
Hint
Hint
Find d from lines/mm, then use nλ = d sinθ with n=1.
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Question
Determine the maximum number of orders that can be observed with this grating and wavelength.\n[3]
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Hint
Hint
Use sinθ≤1 in nλ=d sinθ and take floor.
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Question
Calculate the angular separation of the first-order maxima for wavelengths 589.0 nm and 589.6 nm.\n[2]
Hint
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Hint
Find θ for each then subtract.
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Question
Outline how increasing the number of lines per millimeter of the grating affects the angular separation.\n[1]
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Hint
More lines/mm → smaller d → larger θ → larger separation.
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Complete Answer
Increasing lines/mm decreases d, which increases θ for each wavelength; hence the angular separation increases.
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