The EM wave from air enters a medium. The electric fields are $E_1 = E_{01} \hat{x} \cos [ 2 \pi v (\frac{z}{c} - t)]$ in air and $E_2 = E_{02} \hat{x} \cos [k(2z - ct)]$ in medium, where the wave number $k$ and frequency $v$ refer to their values in air. The medium is non-magnetic. If $\in_{r_1}$ and $\in_{r_2}$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

Question

( A ) $\frac{\in_{r_1}}{\in_{r_2}} = 2$
( B ) $\frac{\in_{r_1}}{\in_{r_2}} = \frac{1}{2}$
( C ) $\frac{\in_{r_1}}{\in_{r_2}} = 4$
( D ) $\frac{\in_{r_1}}{in_{r_2}} = \frac{1}{4}$