An EM wave from air enters a medium

PHYSICS · Single correct · CBSE · Physics · Electromagnetic Waves · Electromagnetic Waves

Problem

An EM wave from air enters a medium. The electric fields are

\vec{E}_1 = E_{01} \hat{x} \cos \left[ 2\pi v \left( \frac{z}{c} - t \right) \right]

in air and

\vec{E}_2 = E_{02} \hat{x} \cos[k(2z - ct)]

in medium, where the wave number

k

and frequency

v

refer to their values in air. The medium is nonmagnetic. If

\epsilon_r

and

\epsilon_{r2}

refer to relative permittivities of air and medium respectively, which of the following options is correct? (1)

\frac{\epsilon_{r1}}{\epsilon_{r2}} = 4

(2)

\frac{\epsilon_{r1}}{\epsilon_{r2}} = 2

(3)

\frac{\epsilon_{r1}}{\epsilon_{r2}} = \frac{1}{4}

(4)

\frac{\epsilon_{r1}}{\epsilon_{r2}} = \frac{1}{2}