Chapter 36, Problem 36.53P

CALC The intensity of light in the Fraunhofer diffraction pattern of a single slit is given by Eq. (36.5). Let γ = β/2. (a) Show that the equation for the values of γ at which I is a maximum is tan γ = γ. (b) Determine the two smallest positive values of γ that are solutions of this equation. (Hint: You can use a trial-and-error procedure. Guess a value of γ and adjust your guess to bring tan γ closer to γ. A graphical solution of the equation is very helpful in locating the solutions approximately, to get good initial guesses.) (c) What are the positive values of γ for the first, second, and third minima on one side of the central maximum? Are the γ values in part (b) precisely halfway between the γ values for adjacent minima? (d) If a = 12λ, what are the angles θ (in degrees) that locate the first minimum, the first maximum beyond the central maximum, and the second minimum?