A layer of a lossless medium, 1 m in thickness, with a refractive index n = 4, is placed between an air-filled half-space and an ideally conducting plane (located at x 1 = 0). A uniform plane wave, at...

A layer of a lossless medium, 1 m in thickness, with a refractive index n = 4, is placed between an air-filled half-space and an ideally conducting plane (located at x₁
= 0). A uniform plane wave, at a frequency f = 6 GHz, impinges from air, travels through the layer, and is reflected back. Find the period of the standing wave in the dielectric layer, along the x₁
direction, for the following cases:

a) incidence along the x₁
axis;

b) incidence along a direction such that the refracted wave in the layer travels at 45 degrees with respect to the x₁
axis;

c) incidence at an angle (in air) of 45 degrees with respect to the x₁
axis.