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In this problem we will consider an electromagnetic wave propagating in a nonmag- netic, lossless dielectric. The dielectric has a refractive index of 1.5, and the wave is a uniform plane electromagnetic wave propagating in the 2-direction. The electric field phasor associated with the wave is given by: E(z) = (x +3jy) e -j2000πz - V/m (a) Find the relative permittivity and intrinsic impedance of the dielectric. (b) Find the frequency of the electromagnetic wave. (c) Now let's consider Scenario 1, as depicted on the left in the figure below. Here, the dielectric material stops and terminates in free space at the position z = 0. The electromagnetic wave hits this interface with free space at normal incidence. Write an expression for the total electric field phasor in the dielectric and in free space. Scenario 1 Scenario 2 dielectric dielectric na = 1.5 free space n = 1 na = 1.5 45° free space incident light incident light n = 1 Ix Z Z z = 0 z=0 (d) Consider your answer from part (c). What is the time-average power density carried by: i) the incident wave, ii) the reflected wave, and iii) the transmitted wave? (e) Now consider your answers from parts (c) and (d). What were the reflection and transmission coefficients associated with the wave in part (c)? Briefly explain why I2 + 7² 1 and yet power is still conserved. T

The final two parts of this problem will be worth 1 pt. For these parts, we will consider Scenario 2, as depicted on the right side of the figure above. Here, the dielectric material stops and terminates in free space; however, this interface makes a 45° angle with the x and z axes, as shown above. (f) What fraction of the incident light power is reflected? (g) What is the polarization of the reflected wave? (Specify whether the polarization is linear, circular, or elliptical, and, if applicable, specify right or left handed.)