An electromagnetic wave of frequency 3, GHz enters a dielectric medium of relative electric per

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8.Electromagnetic waves

hard

An electromagnetic wave of frequency $3\, GHz$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be $.......\,\times 10^{-2} \, cm$

A

$667$

B

$577$

C

$627$

D

$747$

(JEE MAIN-2021)

Solution

$\lambda$ in vacuum $=\frac{c}{f}=\frac{3 \times 10^{8}}{3 \times 10^{9}}=0.1\, m$

$\therefore \lambda$ in medium $=\frac{0.1}{\mu}$

Where refractive index

$\mu=\sqrt{\mu_{z} \varepsilon_{z}}$

Assuming non-magnetic material $\mu_{ r }=1$

$\therefore \quad \mu=\sqrt{2.25}=1.5$

$\lambda_{ m }=\frac{0.1}{1.5}=\frac{1}{15} m =6.67 \,cm$

$=667 \times 10^{-2}\, cm$

Standard 12

Physics

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