An EM wave from air enters a medium. The electric fields are ${\overrightarrow{E}}_1=E_{01}\widehat{x}\cos \left[2\pi v\left(\frac{z}{c}-t\right)\right]$ in air and ${\overrightarrow{E}}_2=E_{02}\widehat{x}\cos \left[k\left(2z-ct\right)\right]$in medium, where the wave number k and frequency $v$ refer to their values in the air. The medium is non-magnetic. If ${ϵ}_{r_1}$ and ${ϵ}_{r_2}$ refer to relative permittivities of air and medium respectively, which of the following options, is correct?

• A

  $\frac{{ϵ}_{r_1}}{{ϵ}_{r_2 }}=\frac{1}{2}$
• B

  $\frac{{ϵ}_{r_1}}{{ϵ}_{r_2 }}=4$
• C

  $\frac{{ϵ}_{r_1}}{{ϵ}_{r_2 }}=2$
• Correct answer
  D

  $\frac{{ϵ}_{r_1}}{{ϵ}_{r_2 }}=\frac{1}{4}$

Hence, the correct answer is option: 'D'.