Q.Monochromatic light of wavelength $\lambda$ is incident normally on a single slit of width $a$, and the diffraction pattern is observed on a screen at a distance $D$. Derive an expression for the total width of the central maximum of the pattern, and state how this width compares with the spacing of the secondary maxima on either side.

For a single slit of width a illuminated by a plane wavefront, dividing the slit into pairs of matching sub-sources shows that whenever the path difference between the two extreme edge rays, $a\sin\theta$, equals a whole wavelength $n\lambda$, the ENTIRE slit's light cancels in matching pairs, giving a diffraction MINIMUM at $a\sin\theta=n\lambda$. The (approximate) maxima fall roughly midway between successive minima, near $a\sin\theta=(n+\tfrac12)\lambda$. Using the small-angle approximation ($D\gg a$), this gives fringe spacing $W=\lambda D/a$ -- identical in FORM to Young's double-slit fringe width, but with slit WIDTH a replacing slit SEPARATION d -- with the crucial exception that the central bright fringe is TWICE as wide, $2\lambda D/a$, as every other fringe, since it spans between the first minima on either side. …