3. A beam of monochromatic light is incident normally on a diffraction grating. The grating has 300 lines per millimetre. A third-order maximum is observed at an angle of 35° to the normal.
(a) Calculate the spacing between the lines on the grating. [1]
(b) Calculate the wavelength of the light. [2]
(c) Determine the highest order maximum that can be observed with this grating and wavelength. [3]
Question
Calculate the spacing between the lines on the grating. [1]
Hint
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The spacing ‘d’ is the reciprocal of the number of lines per unit length. Ensure you convert units correctly (mm to m).
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\(d = 3.33 × 10^{-6}\) m
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Question
Calculate the wavelength of the light. [2]
Hint
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Use the diffraction grating equation \(d \sin \theta = n\lambda\). You know d, n, and θ.
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\(\lambda = 6.37 × 10^{-7}\) m (or 637 nm)
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Question
Determine the highest order maximum that can be observed with this grating and wavelength. [3]
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The maximum possible angle for diffraction is 90 degrees, where sin θ = 1. Use this limiting condition in the grating equation to find the maximum possible value for n.
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Highest order = 5
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