Question

An electromagnetic wave of frequency $3.0 \,MHz$ passes from vacuum into a non-magnetic medium with permittivity, $\epsilon=16\, \epsilon_{0} .$ Where, $\epsilon_{0}$ is the free space permittivity. The change in wavelength is

• A. -75 m
• B. +75 m
• C. -50 m
• D. +50 m

Answer 1

Answer: (A)

Given, frequency of EM wave,
$f =3 \,MHz $
$=3 \times 10^{6} Hz$
and permittivity of non-magnetic medium,
$\varepsilon=16 \varepsilon_{0}$
Wavelength of EM wave,
$\lambda=\frac{c}{f}=\frac{3 \times 10^{8}}{3 \times 10^{6}} $
$\lambda=100\, m$
Velocity of electromagnetic $(EM)$ into non-magnetic material,
$v =\frac{c}{\sqrt{\varepsilon_{r}}}=\frac{3 \times 10^{8}}{\sqrt{16}} \,\,\left[\because \varepsilon_{r}=\frac{\varepsilon}{\varepsilon_{0}}=16\right] $
$=\frac{3}{4} \times 10^{8} \,m / s $
$\therefore $ Wavelength, $\lambda^{'}=\frac{v}{f}=\frac{\frac{3}{4} \times 10^{8}}{3 \times 10^{6}}=25\, m$
$\therefore $ Change in wavelength $=\lambda^{\prime}-\lambda$
$=25-100=-75\, m$