Chapter 37, Problem 53CP

Consider a light wave passing through a slit and propagating toward a distant screen. Figure P37.53 shows the intensity variation for the pattern on the screen. Give a mathematical argument that more than 90% of the transmitted energy is in the central maximum of the diffraction pattern. Suggestion: You are not expected to calculate the precise percentage, but explain the steps of your reasoning. You may use the identification

$\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\cdots =\frac{{\pi }^2}{8}$

Figure P37.53