Discuss the special cases on first minimum in Fraunhofer diffraction.

Explanation

Let us consider the condition for first minimum with `(n = 1). A sin theta = lambda`
The first minimum has an angular spread of, `sin theta = (lambda)/(a)`. Special cases to discuss on the condition.
(i) When `a lt lambda`, the diffraction is not possible, because `sin theta` can never be greter than I.
(ii) Whe `a ge lambda`, the diffraction is possible.
(1) For `a = lambda, sin theta = 1 i.e. theta = 90^(@)`. That means the first minimum is at `90^(@)` Hence, the central maximum spreads fully in to the geometrically shadowed region leading to bending of the diffracted light to `90^(@)`
(2) For `agt gtlamda,sinthetaltlt1` i.e. the first minimum will fall within the width of the slit itself. The diffraction will not be noticed at all.
(iii) When `a gt lambda` and also comparable, say `a=2lambda,sintheta=(lambda)/(a)=(lambda)/(2lambda)=(1)/(2),thentheta=30^(@)`. These are practical cases where diffraction could be observed effectively.