1. A plane electromagnetic wave of angular frequency 
is
incident perpendicularly on the surface of a non-magnetic medium of
dielectric constant 
. To keep the notation uniform, assume that
the wave propagates in the z direction and that the incident electric
field is in the x direction (or use vector methods that are
coordinate-independent).
(a) Find the reflected electric and magnetic fields.
(b) Find the electric and magnetic fields in the medium.
(c) Find the reflection coefficient R, i. e. the ratio of reflected to incident intensity.
(d) Find the transmission coefficient T, i. e. the ratio of transmitted to incident intensity, by computing the Poynting vector just inside the medium.
(e) Verify that R + T = 1 for any 
,
real or complex.
(f) (For complex 
) compute the average power dissipated
in the medium as the integral of 
, with 
. Show that it is equal to the
average incident power times the coefficient T computed in part
(d).
2. A plane electromagnetic wave of angular frequency 
is
incident perpendicularly on the surface of a non-magnetic medium of
dielectric constant 
. Compute the pressure exerted on the surface
by the wave and discuss in particular the limit of perfect reflection.
3. For a medium with vanishing d.c. conductivity and 
(a) Write down Kramers-Kronig relations for the index of refraction n
(b) Obtain a sum rule for 
Im n.
4. Jackson's problem 7.16