Chapter 36, Problem 36.67CP

CALC Intensity Pattern of N Silts, 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 N²I₀ (b) The principal maximum at the center of the pattern extends from ϕ = −2π/N to ϕ = 2π/N, so its width is inversely proportional to 1/N. (c) A minimum occurs whenever is an integral multiple of 2π/N. except when ϕ is an integral multiple of 2π (which gives a principal maximum), (d) There are (N − 1) minima between each pair of principal maxima, (e) Halfway between two principal maxima. Use intensity can be no greater than I₀; that is, it can be no greater than 1/N² times the intensity at a principal maximum.