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

• A
  $\frac{\varepsilon_{r_1}}{\varepsilon_{r_2}} = 2$
• B
  $\frac{\varepsilon_{r_1}}{\varepsilon_{r_2}} = \frac{1}{4}$
• C
  $\frac{\varepsilon_{r_1}}{\varepsilon_{r_2}} = \frac{1}{2}$
• D
  $\frac{\varepsilon_{r_1}}{\varepsilon_{r_2}} = 4$