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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
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The correct answer is:
1.5
Frequency of light wave, \(v=4 \times 10^{14} \mathrm{~Hz}\) Wavelength, \(\lambda_m=5 \times 10^{-7} \mathrm{~m}\)
Wavelength of light wave in air
\(\begin{aligned}
\lambda_{\text {air }} & =\frac{\text { Velocity of light in air }}{\text { Frequency of light }}=\frac{3 \times 10^8}{4 \times 10^{14}} \\
& =7.5 \times 10^{-7} \mathrm{~m}
\end{aligned}\)
\(\therefore\) Refractive index of medium is given as
\(\mu=\frac{\lambda_{\text {air }}}{\lambda_{\text {medium }}}=\frac{7.5 \times 10^{-7}}{5 \times 10^{-7}}=1.5\)
Wavelength of light wave in air
\(\begin{aligned}
\lambda_{\text {air }} & =\frac{\text { Velocity of light in air }}{\text { Frequency of light }}=\frac{3 \times 10^8}{4 \times 10^{14}} \\
& =7.5 \times 10^{-7} \mathrm{~m}
\end{aligned}\)
\(\therefore\) Refractive index of medium is given as
\(\mu=\frac{\lambda_{\text {air }}}{\lambda_{\text {medium }}}=\frac{7.5 \times 10^{-7}}{5 \times 10^{-7}}=1.5\)
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