Chapter 37, Problem 47AP

The intensity of light in a diffraction pattern of a single slit is described by the equation

$I={\mathrm{I}}_{\text{max}}\frac{{\sin }^2\varphi }{{\varphi }^2}$

where ϕ = (πa sin θ)/λ. The central maximum is at ϕ = 0, and the side maxima are approximately at $\varphi =(m+\frac{1}{2})\pi$ for m = 1, 2, 3, …. Determine more precisely (a) the location of the first side maximum, where m = 1, and (b) the location of the second side maximum. Suggestion: Observe in Figure 37.6a that the graph of intensity versus ϕ has a horizontal tangent at maxima and also at minima.