Chapter 36, Problem 17P

(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 α and equating the result to zero, obtaining the condition tan α = α. To find values of a satisfying this relation, plot the curve y = tan a and the straight line y = α and then find their intersections, or use a calculator to find an appropriate value of α by trial and error. Next, from α = (m + )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 α and (c) associated m, the (d) second smallest a and (e) associated m, and the (f) third smallest α and (g) associated m?