**True or False:** EM Waves can have velocities higher than $c$. 1. True 2. False 3. I don't know what to believe anymore Note: * Correct answer: A

## Announcements * Quiz 6 (Next Friday) * Given two infinite plane waves at different frequencies, determine the resulting wave in a "good conductor" * Sketch the waves in free space and in the conductor * Discuss the implications from your analysis

Given two waves, $f_1(t) = A \cos (\omega_1 t)$ and $f_2(t) = A \cos (\omega_2 t)$, let's propose an average frequency: $\omega_a = \frac{1}{2}(\omega_1+\omega_2)$ and a modulation frequency: $\omega_m = \frac{1}{2}(\omega_1-\omega_2)$. How can you write $\omega_1$ and $\omega_2$ in terms of these frequencies? 1. $\omega_1 = \omega_a - \omega_m \qquad \omega_2 = \omega_a + \omega_m$ 2. $\omega_1 = \omega_a + \omega_m \qquad \omega_2 = \omega_a - \omega_m$ 3. $\omega_1 = \frac{\omega_a + \omega_m}{2} \qquad \omega_2 = \frac{\omega_a - \omega_m}{2}$ 4. $\omega_1 = \frac{\omega_a - \omega_m}{2} \qquad \omega_2 = \frac{\omega_a + \omega_m}{2}$ 5. None of these Note: * Correct Answer: B

Given two waves, $f_1(t) = A \cos (\omega_1 t)$ and $f_2(t) = A \cos (\omega_2 t)$, which of the following correspond to the total wave, $f_T(t)$? 1. $A \cos (\omega_1 t) + A \cos (\omega_2 t)$ 2. $A^2 \cos (\omega_1 t) \cos (\omega_2 t)$ 3. $2A \cos ((\omega_1+\omega_2) t)\cos((\omega_1-\omega_2)t)$ 4. $2A \cos (\frac{(\omega_1+\omega_2)}{2} t)\cos(\frac{(\omega_1-\omega_2)}{2} t)$ 5. More than one of these Note: * Correct Answer: E (it's A and D)

For our atomic model of permittivity we found $\widetilde{\varepsilon}$ to be $$\widetilde{\varepsilon} = \varepsilon_0\left(1+\dfrac{Nq^2}{\varepsilon_0 m}\sum_i \dfrac{f_i}{(\omega_i^2-\omega^2)-i\gamma_i\omega}\right)$$ We also know that $\dfrac{n}{c} = \dfrac{\widetilde{k}}{\omega} = \sqrt{\widetilde{\varepsilon}\mu}.$ * Find (and simplify) a formula for $n$, assuming the term adding to "1" above is small. * In that limit, find $k_R$ and $k_I$. What does each one tell you, physically? * Sketch both of these as functions of $\omega$ (assuming that only one term in that sum "dominates")