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  • 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 _______<img alt="\times 10^{-2}cm." src="https://entrancecorner.codecogs.com/gi

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.
Option: 1 667
Option: 2 337
Option: 3 227
Option: 4 447

Answers (1)

best_answer

wavelength (\lambda )in vacuum

\begin{array}{l} =\frac{c}{f}=\frac{3 \times 10^{8}}{3 \times 10^{9}}=0.1 \mathrm{~m} \\ \end{array}\begin{array}{l} \lambda =\frac{c}{f}=\frac{3 \times 10^{8}}{3 \times 10^{9}}=0.1 \mathrm{~m} \\ \end{array}

\therefore \lambda \text { in medium }=\lambda _m=\frac{0.1}{\mu}

Where refractive index=\mu=\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}}

Assuming non-magnetic material \Rightarrow \mu_{\mathrm{r}}=1
 \begin{aligned} \therefore \quad & \mu=\sqrt{2.25}=1.5 \\ \Rightarrow \lambda_{\mathrm{m}} &=\frac{0.1}{1.5}=\frac{1}{15} \mathrm{~m}=6.67 \mathrm{~cm} =667 \times 10^{-2} \mathrm{~cm} \end{aligned}

 

Posted by

avinash.dongre

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