Problem 3 (20 pts) Suppose a plane wave is incident on the smooth dielectric halfspace at an angle de = pi/3. The dielectric constant of the air is cair = 60, where co is the vacuum dielectric constant. The relative dielectric constant of the halfspace is er = 360. The conductivity is neglected. Please answer the following questions. (4 pts)(a) Compute the angle of the reflected and transmitted wave using Snell's law. (6 pts) (b) Compute the reflection and transmission coefficients for both TE and TM waves. (6 pts) (c) Now, suppose that we have a rough surface where Kirchhoff The- ory can be applied. First, explain the underlying assumption for applying the Kirchhoff Theory. Then, compute the reflection coefficients for both TE and TM waves, given that the height distribution is Gaussian with standard devia- tion oh = 3. (4 pts)(d) Following (c), find the reflection coefficients for TE and TM waves when considering the grazing incidence (Hint: be careful about the angle defi- nition)