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Question
In deriving the single slit diffraction pattern, it was stated that theintensity is zero at angles of nλ/a. Justify this by suitably dividingthe slit to bring out the cancellation.
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Solution
Consider the width of the slit d and it is divided into n smaller slits. Let d ′ be the width of each smaller slit.
The width of each slit is given by,
d ′ = d n n = d d ′ (1)
The angle of diffraction is given as,
θ = n λ d (2)
From equation (1) and (2), we get
θ = d d ′ λ d θ = λ d ′
The each of infinitesimally slits sends zero intensity in the θ direction.
Thus, the combinations of these slits give zero intensity.
Consider the width of the slit
The width of each slit is given by,
The angle of diffraction is given as,
From equation (1) and (2), we get
The each of infinitesimally slits sends zero intensity in the
Thus, the combinations of these slits give zero intensity.
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