EE 320 Homework 07 1. Consider the plane electromagnetic wave in vacuum (in SI units) given by the expressions Ex = -3 cos[21 x 1014 (t -) + 7] , By = 3V3 cos[2nt X 1014 (t - 2) + "], and Ez = 0, where c = 3 x 105 m/s (a) What are the frequency, wavelength, propagation direction, and amplitude of the wave? (b) Write an expression for the magnetic flux density B. 2. An electromagnetic plane wave is specified (in SI units) by E = -62 . eil(v3x+y)mx107-9.42x1015t] Find (a) the amplitude of the electric field, (b) the wave propagation direction, (c) the propagation constant and the wavelength, (d) the frequency and the angular frequency, and (e) the phase velocity. 3. Write expressions for E and H fields that constitute a plane wave of angular frequency @ and propagation constant k, traveling in the positive z-direction. The electric field of wave oscillates in the plane tilted +30 away from the x-axis. 4. A 550-nm plane wave of light whose electric field is in the z-direction is travelling in the y-direction in vacuum. (a) What is the frequency f of the wave? (b) What is the w and k of the wave? (c) If the electric field amplitude is 300 V/m, what is the amplitude of the magnetic field? (d) Write expressions for both E(r, t) and H(r, t) given that each is zero at T = (0, 0, 0) and t = 0. Put in all the appropriate units. 5. A monochromatic laser beam polarized with its electric field perpendicular to the plane of incidence impinges normally in air on glass (nglass = 1.50). Determine the reflection and transmission coefficients. Redo the calculation with the same beam going normally from glass to air. 6. Light is incident in air on the flat surface of a sheet of glass of index 1.60 at an angle of 30.0 to the normal. What are the reflection and transmission coefficients for both s- and p- linear polarizations, respectively? In addition, calculate RI, Ry, Ti, TH. 7. Which physical effect can explain the phenomenon shown in the figure below? Which direction the polarizer should be oriented in order to have the effect? If the refractive index of the water is /water = 1.33, what angle of light incidence will make the phenomenon most significant? unpolarized polarized 8. Linearly polarized light beam with its E-field perpendicular to the plane of incidence is incident normally in air on an air-glass interface where /glass = 1.5. If the irradiance of transmitted light measured is 800 W/m, how much is reflected? 9. Show that energy during reflection and transmission processes is conserved, i.e. RI+ Ty = 1, R1 + 1 = 1, using the Fresnel equations (assuming ni, nt ER)