An EM wave from air enters a medium. The electric fields are \(\overrightarrow {{E_1}}  = {E_{01}}\hat x\;cos\left[ {2\pi v\left( {\frac{z}{c} - t} \right)} \right]\) in air and \(\overrightarrow {{E_2}}  = {E_{02}}\hat x\;cos\left[ {k\left( {2z - ct} \right)} \right]\) 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?

1. A \(\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = 2\)
2. B \(\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = \frac{1}{4}\)
3. C \(\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = \frac{1}{2}\)
4. D \(\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = 4\)