Question

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

Answer 1

${ϵ}_{\text{r}}=2.25$

Assuming non-magnetic material, ${\mu }_{\text{r}}=1$

Hence refractive index of medium $\sqrt{{\mu }_{\text{r}}{ϵ}_{\text{r}}}=1.5$

$\therefore \frac{{\lambda }_{\text{v}}}{{\lambda }_{\text{m}}}=n$

${\lambda }_{\text{m}}=\frac{c}{f_{\text{n}}}=\frac{3\times {10}^8}{3\times {10}^9\times 1.5}=\frac{2}{3}\times {10}^{-1}\text{m}$

${\lambda }_{\text{m}}=\frac{20}{3}\text{cm}=667\times {10}^{-2}\text{cm}$