Halliday, Resnick & Walker — Interference: Problem 44

44 In the two-slit experiment of Fig. 35-10, let angle \(\theta\) be \(30.0^\circ\), the slit separation be \(4.24 \text{ } \mu\text{m}\), and the wavelength be \(\lambda = 500 \text{ nm}\). (a) What multiple of \(\lambda\) gives the phase difference between the waves of rays \(r_1\) and \(r_2\) when they arrive at point \(P\) on the distant screen? (b) What is the phase difference in radians? (c) Determine where in the interference pattern point \(P\) lies by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies.