Two plane waves that are spatially and temporally coherent propagate in the x-z plane and intersect at an angle such that each wave makes an angle (please see the attached file) with the z-axis. The figure below shows the k-vectors associated with the two beams.
a) Recall that the general expression for E_+ and E. by writing and (please see the attached file) in terms of (please see the attached file). Assume you are looking at the electric field at some arbitrary location and that the amplitude is the same for both fields.
b)Determine the intensity at (please see the attached file) and show that the intensity only varies in x.
c) The distance between two bright or two dark fringes is called the fringe spacing and is denoted by (please see the attached file). Show that (please see the attached file).
d) What are some of the interesting limiting values of (please see the attached file) and do they make sense physically (i.e. from the physical set-up (choose 2 or 3)? What would you expect to see on a screen in each case?
e) The eye has an angular resolution of about 0.01^0. If you are standing 1 foot away from a screen that allows you to see the interference pattern, what is the largest/smallest angle that the two plane waves can have such that you eye can still make out the fringes.