(a) Show that the values of a at which intensity maxima for single-slit diffraction occur can be found exactly by differentiating Eq. 36-5 with respect to a and equating the result to zero, obtaining the condition tan a = a. To find values of a satisfying this relation, plot the curve y = tan a and the straight line y = a and then find their intersections, or use a calculator to find an appropriate value of a by trial and error. Next, from a =(m + ½)π, determine the values of m associated with the maxima in the single-slit pattern. (These m values are not integers because secondary maxima do not lie exactly halfway between minima.) What are the

(b) Smallest a and

(c) Associated m, the

(d) Second smallest a and

(e) Associated m, and the

(f) Third smallest a and

(g) Associated m?