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JEE PHYSICS MCQ: ELECTROMAGNETIC WAVES

1 Medium
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Analyzing +4 | -1
An EM wave from air enters a medium. The electric fields are E1=E01x^cos⁡[2πv(zc−t)]{E_1} = {E_{01}}\hat x\cos \left[ {2\pi v\left( {\frac{z}{c} - t} \right)} \right] in air and E2=E02x^cos⁡[k(2z−ct)]{E_2} = {E_{02}}\hat x\cos \left[ {k\left( {2z - ct} \right)} \right] in medium, where the wave number k and frequency ν refer to their values in air. The medium is non-magnetic.
If εr1{\varepsilon _{{r_1}}} and εr2{\varepsilon _{{r_2}}} refer to relative permittivities of air and medium respectively, which of the following options is correct?
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Correct option: C
εr1εr2=14\frac{{{\varepsilon _{{r_1}}}}}{{{\varepsilon _{{r_2}}}}} = \frac{1}{4}
Option C (εr1εr2=14\frac{{\varepsilon _{{r_1}}}}{{\varepsilon _{{r_2}}}} = \frac{1}{4}) is correct because the ratio of relative permittivities is inversely proportional to the square of the ratio of speeds.

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