Discuss diffraction at single slit and obtain the consition for `n^(th)` minimum. Diffraction at single slit:

Explanation

(i) For points of maxima, the slit is to be divided in to odd number of equal parts so that one part remains un-cancelled making the point P appear bright. The condition for first maximum is,
` a/3 sin theta = lamda/2 "or " a sin theta = (3 lamda)/(2)`
The condition for second maximum is,
` a/5 sin theta = lamda/2 " or " a sin theta = (5 lamda)/(2)`
The condition for third maximum is,
`a/7 sin theta = lamda/2 " or " sin theta = (7lamda)/(2)`
In the same way, condition for nth maximum is,
` a sin theta = ( 2n + 1) lamda/2 ` (nth maximum)
where, n = 0, 1, 2, 3, ..., is the order of diffraction maximum.
(ii) The central maximum is called `0^(th)` order maximum. The points of the maximum intensity lie nearly midway between the successive minima.