Solved: Intensity Pattern of N Slits, Continued. Part (d)

Chapter 36, Problem 36.67

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Intensity Pattern of N Slits, Continued. Part (d) of Challenge Problem 36.66 gives an expression for the intensity in the interference pattern of N identical slits. Use this result to verify the following statements. (a) The maximum intensity in the pattern is \(N^2 I_0\). (b) The principal maximum at the center of the pattern extends from \(\phi=-2 \pi / N\) to \(\phi=2 \pi / N\), so its width is inversely proportional to 1/N. (c) A minimum occurs whenever \(\phi\) is an integral multiple of \(2 \pi / N\), except when \(\phi\) is an integral multiple of \(2 \pi\) (which gives a principal maximum). (d) There are (N-1) minima between each pair of principal maxima. (e) Halfway between two principal maxima, the intensity can be no greater than \(I_0\); that is, it can be no greater than \(1 / N^2\) times the intensity at a principal maximum.