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2009 Question 7.
When light shines on a compact disc it acts as a diffraction grating causing diffraction and dispersion of
the light.
(i) Explain diffraction
Diffraction is the spreading out of a wave when it passes through a gap or passes by
an obstacle.
(ii) Explain dispersion.
Dispersion is the splitting up of white light into its constituent colours.
(iii)Derive the diffraction grating formula.
For constructive interference path difference = nλ, where n is an integer
From diagram we can see that path difference = d sin θ
nλ = d sin θ
(iv) An interference pattern is formed on a screen when green light from a laser passes normally through a
diffraction grating. The grating has 80 lines per mm and the distance from the grating to the screen is 90
cm. The distance between the third order images is 23.8 cm.
Calculate the wavelength of the green light.
d = 1/80000 = 1.25 × 10-5 m
θ = tan-1 (0.238/0.90)
n = 3
nλ = d sin θ λ = d sin θ/n λ = 551 (± 5) × 10-9 m.
(v) Calculate the maximum number of images that are formed on the screen.
For maximum number θ = 900 sin θ = 1
nλ = d sin θ nλ = d n= d/λ
n = 22.7 so the greatest whole number of images is 22.
But this is on one side only.
In total there will be 22 on either side, plus one in the middle, so total = 45
(vi) The laser is replaced with a source of white light and a series of spectra are formed on the screen.
Explain how the diffraction grating produces a spectrum.
Different colours have different wavelengths so constructive interference occurs at different positions for
each separate wavelength.
(vii) Explain why a spectrum is not formed at the central (zero order) image.
At central image θ = 0 so constructive interference occurs for all separate wavelengths at the same point
so no separation of colours.
