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?
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?
- [JEE MAIN 2018]
- A
$\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = 2$
- B
$\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = \frac{1}{4}$
- C
$\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = \frac{1}{2}$
- D
$\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = 4$
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- [JEE MAIN 2022]