Solved: The intensity of light in the Fraunhofer

Chapter 36, Problem 36.53

(choose chapter or problem)

The intensity of light in the Fraunhofer diffraction pattern of a single slit is given by Eq. (36.5). Let g = b>2. (a) Show that the equation for the values of g at which I is a maximum is tang = g. (b) Determine the two smallest positive values of g that are solutions of this equation. (Hint: You can use a trial-anderror procedure. Guess a value of g and adjust your guess to bring tang closer to g. 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 g for the first, second, and third minima on one side of the central maximum? Are the g values in part (b) precisely halfway between the g values for adjacent minima? (d) If a = 12l, what are the angles u (in degrees) that locate the first minimum, the first maximum beyond the central maximum, and the second minimum?