Question

The electric field of a plane electromagnetic wave in a medium is given by

where c is the speed of light in free space. E field is polarized in the x −z plane. The speed of the wave is v in the medium. Then:

• A. \( \hat{n} = \hat{i} - \hat{k}; \quad v = c \)
• B. \( \hat{n} = \frac{\hat{i} - \hat{k}}{\sqrt{2}}; \quad v = \frac{c}{\sqrt{3}} \)
• C. Refractive index of the medium is \(\sqrt{3}\)
• D. \( \hat{n} = \frac{\hat{i} + \hat{k}}{\sqrt{2}}; \quad v = \frac{c}{2} \)

Hint:

In electromagnetic waves, the wave vector direction k determines the direction of prop agation, and the polarization direction ˆn is perpendicular to both k and the direction of the electric field.