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Q.

An electromagnetic wave of frequency 3GHZ enters into a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be________ $\times 10^{- 2} c m$

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answer is 667.

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Detailed Solution

$λ$ in vacuum
$= \frac{c}{f} = \frac{3 \times 10^{8}}{3 \times 10^{9}} = 0.1 m$
$∴ λ in medium = \frac{0.1}{μ}$
Where refractive index
$μ = \sqrt{μ_{r} ε_{r}}$
Assuming non-magnetic material $μ_{r} = 1$
$∴ μ = \sqrt{2.25} = 1.5 λ_{m} = \frac{0.1}{1.5} = \frac{1}{15} m = 6.67 cm = 667 \times 10^{- 2} cm$

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