A light wave has a frequency of \(4 \times 10^{14} \mathrm{~Hz}\) and a wavelength of \(5 \times 10^{-7}…
A light wave has a frequency of \(4 \times 10^{14} \mathrm{~Hz}\) and a wavelength of \(5 \times 10^{-7} \mathrm{~m}\) in a medium. The refractive index of the medium is
1.5
1.33
1.0
0.66
Solution
$ v = 4 \times 10^{14} \, \text{Hz} $
$ \lambda_m = 5 \times 10^{-7} \, \text{m} $
Frequency of light wave in air
$\begin{aligned}
\lambda_{\text{air}} & =\frac{\text{Velocity of light in air}}{\text{Frequency of light}}=\frac{3 \times 10^8}{4 \times 10^{14}} \\
& =7.5 \times 10^{-7} \, \text{m}
\end{aligned}$
\(\therefore\) Refractive index of medium is given as
\(\mu=\frac{\lambda_{\text {air }}}{\lambda_{\text {medium }}}=\frac{7.5 \times 10^{-7}}{5 \times 10^{-7}}=1.5\)