Topic: Electromagnetics
A uniform plane wave in air impinge at $45^\circ$ angle on a lossless dielectric material with dielectric constante $\epsilon_r$. The transmitted wave propagates in a $30^\circ$ direction with respect to the normal. The value of $\epsilon_r$ is
- A. 1.5
- B. $\sqrt{1.5}$
- C. 2
- D. $\sqrt{2}$
Answer: C. 2
Explanation: According to Snell's law: $n_1\sin\theta_1 = n_2\sin\theta_2$.
For air, $n_1 = \sqrt{\epsilon_{r1}} = 1$.
$\sin 45^\circ = \sqrt{\epsilon_r}\sin 30^\circ$
$\frac{1}{\sqrt{2}} = \sqrt{\epsilon_r} \left(\frac{1}{2}\right)$
$\sqrt{\epsilon_r} = \frac{2}{\sqrt{2}} = \sqrt{2}$.
Squaring both sides gives $\epsilon_r = 2$.