(a) Using Huygens’s construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a monochromatic beam of light is incident normally.
(b) Show that the angular width of the first diffraction fringe is half that of the central fringe.
(c) Explain why the maxima at 
become weaker and weaker with
increasing n.
(a) We can regard the total contributions of the wave front LN at some point P on the screen, as the resultant effect of the superposition of its wavelets like LM, 
, 
. These have to be superposing taking into account their proper phase differences. We therefore, get maxima and minima, i.e. a diffraction pattern, on the screen.
(b) Conditions for first minimum on the screen
Angular width of the central fringe on the screen
Angular width of first diffraction fringe,
Hence angular width of central fringe is twice the angular width of first fringe.
(c) Maxima become weaker and weaker with increasing n. This is because the effective part of the wave front, contributing to the maxima, becomes smaller and smaller, with increasing n.
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