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An electromagnetic wave of frequency $3 MHz$ passes from vacuum into a dielectric medium with relative permittivity $\in_{r} = 4.0$ , then

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Wave length is doubled and frequency remains unchanged

Wave length is doubled and frequency becomes half

Wave length is halved and frequency remains unchanged

Wave length and frequency both remains unchanged

answer is C.

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Detailed Solution

$ν_{medium} = \frac{1}{\sqrt{μ_{0} μ_{r} \in_{0} \in_{r}}} = \frac{c}{\sqrt{μ_{r} \in_{r}}}$

$For dielectric medium, μ_{r} = 1$

$∴ v_{medium} = \frac{c}{\sqrt{\in_{r}}} = \frac{c}{\sqrt{4}} = \frac{c}{2}$

$Wavelength of the wave in medium$

$λ_{medium} = \frac{v_{medium}}{f} = \frac{c}{2 f} = \frac{λ_{vacuum}}{2}$

With change in medium, frequency remains same.

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