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$0.04 \mathrm{~m}$ of glass contains the same number of waves as $0.05 \mathrm{~m}$ of water, when monochromatic light passes through them normally. Refractive index of water is $4 / 3$. Refractive index of glass is
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The correct answer is:
$5 / 3$
If $n$ be the number of waves, then wavelength of light in glass, $\lambda_{g}=\frac{0.04}{n}$ and wavelength of light in water, $\lambda_{w}=\frac{0.05}{n}$ Speed of light in glass, $v_{g}=\lambda_{g} \times f=\frac{0.04 f}{n}$ where, $f=$ frequency of light.
Similarly, speed of light in water, $v_{w}=\lambda_{w} \times f=\frac{0.05 f}{n}$
Relative refractive index
$\begin{aligned}
&=\frac{\mu_{w}}{\mu_{g}}=\frac{v_{g}}{v_{w}}=\frac{0.04 f}{n} \times \\
&=\frac{5}{4} \times \mu_{w}=\frac{5}{4} \times \frac{4}{3}=\frac{5}{3}
\end{aligned}$
Similarly, speed of light in water, $v_{w}=\lambda_{w} \times f=\frac{0.05 f}{n}$
Relative refractive index
$\begin{aligned}
&=\frac{\mu_{w}}{\mu_{g}}=\frac{v_{g}}{v_{w}}=\frac{0.04 f}{n} \times \\
&=\frac{5}{4} \times \mu_{w}=\frac{5}{4} \times \frac{4}{3}=\frac{5}{3}
\end{aligned}$
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