4. The following is the expression for the E-field of an electromagnetic wave traveling in a homogeneous dielectric medium: E=(-100 V/m) ei(kz-vt) where = 1.80 1015 rad/s and k = 1.20 107 rad/m. (a) Determine the associated B-field. (b) Find the index of refraction. (c) Compute the electric permittivity. (d) Draw a diagram showing Eo, Bo, and k, the propagation vector. (8 Points) 5. Describe completely the state of polarization of each of the following waves: (12 Points) (a) E = Eo sin 2(z/ - vt) - Eo sin 2(z/ - vt) (b) E Eo cos (kz - oot) - Eo cos (kz - ot) (c) E = Eo cos (cot - kz) + Eo cos (ot - kz + /2). = (d) Et Eo sin (oot - kz) + Eo sin (oot - kz - /4) 6. Imagine that you have two identical perfect linear polarizers and a source of natural light. Place them one behind the other and position their transmission axes at 0 and 50, respectively. Now insert between them a third linear polarizer with its transmission axes at 25. If 800 W/m of light is incident, how much light will emerge with and without the middle polarizer in place? (5 Points) = 7. A light ray is incident in water (nw = 1.33) at an angle of 35 on an interface with flint glass (ng 1.6). Compute the transmission angle. If a ray is incident on the same interface but from the glass side and if the transmission angle needs to be 35, calculate the angle of incidence. (5 Points) 8. Unpolarized light is incident in air on the flat surface of a sheet of glass (refractive index nglass = 1.6) at an angle of 30.0 to the normal. Determine both amplitude coefficients (Fresnel coefficients) of reflection for a TE or TM-polairzed incident wave. What is the significance of the signs of the reflection coefficients? (5 Points)