Monochromatic light of wavelength \(633\,nm\) is incident normally on a diffraction grating. The angle between the central maximum and the second-order maximum is \(35.0°\).
(a) Determine the number of lines per millimetre for this grating. [4]
(b) Calculate the angle at which the first-order maximum is observed. [2]
(c) The light source is replaced with one emitting light of wavelength \(450\,nm\). Describe the change, if any, in the position of the central maximum and the first-order maximum. [2]
Question
Determine the number of lines per millimetre for the grating. [4]
Hint
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Hint
Apply \(n\lambda = d\sin\theta\) with n = 2 to find the grating spacing and then convert to lines per mm.
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\(\approx 453\,\text{lines/mm}\)
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Question
Calculate the angle at which the first-order maximum is observed. [2]
Hint
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Hint
For n = 1, apply the diffraction equation to find \(\sin\theta\) and then determine \(\theta\).
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\(\theta \approx 16.7°\)
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Question
Describe the change, if any, in the position of the central maximum and the first-order maximum when the wavelength is changed to 450 nm. [2]
Hint
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Remember that the central maximum (n = 0) remains fixed at 0° while the first-order maximum is affected by wavelength changes.
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The central maximum remains at \(0°\), and the first-order maximum shifts to a smaller angle because \(450\,nm\) is shorter than \(633\,nm\).
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