Problem 1. Interference in 1D. Two coherent sources SI and 5'2 emit electromagnetic waves of wave- length A. Source 31 is xed at the origin. Source .92 is on a circle of radius R = 3A centered on the origin and can be rotated in the :r 1,: plane to change the angle 3 it makes with the :3 axis. We want to determine the interference pattern very far from the sources so that the plane waves from each are moving parallel to the 1' axis as shown. (a) \"'hat is the phase difference between two waves traveling parallel to the x-axis as a function of S? (1)) Write a condition that must be satised for there to be an intensity maximum at the detector as a function of 9. (c) As 3 increases from C! to 171' how many maxima in intensity are found? For Parts (d) and (e), assume that the peel: electric elds of the plane waves from each source have the same value ED, and that they travel through vacuum. Recall that the intensity of electromagnetic radiation is the energy transported by the wave per unit area per unit time. (d) What is the time-averaged intensity In of the wave from source S1, in terms of EU and fundamental constants? (e) What is ratio of the intensity at the maxima you found in Part (c) to In. 5'2 . To detector, innitely far away. +m