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Question
Show that the angular width of the first diffraction fringe is half that of the central fringe.
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Solution
Let λ and a be the wavelength and slit width of diffracting system, respectively. Let O be the position of central maximum. Condition for the first minimum is given by
asinθ=mλ .....(1)
Let θ be the angle of diffraction.
As diffraction angle is small
∴ sinθ ≈ θ
For the first diffraction minimum, let θ = θ1
For the first minimum, take m =1
aθ1=λ
`=>theta_1=lambda/a`
Now, angular width AB = θ1
Angular width BC = θ1
Angular width AC = 2θ1
Width of central maximum = 2θ1
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