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A monochromatic ray of light travels through glass slab and water column. The number of waves in glass slab of thickness 4 $\mathrm{cm}$ is the same as in water column of height $5 \mathrm{~cm}$. If refractive index of glass is $\frac{5}{3}$, then refractive index of water is
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The correct answer is:
1.33
If the number of waves in $\mathrm{N}$, then the wavelength in water is $\frac{5}{\mathrm{~N}} \mathrm{~cm}$ and wavelength in glass is $\frac{4}{\mathrm{~N}} \mathrm{~cm}$.
$\begin{aligned}
& \lambda_{\mathrm{w}}=\frac{5}{\mathrm{~N}}, \quad \lambda_{\mathrm{g}}=\frac{4}{\mathrm{n}} \\
& { }_{\mathrm{w}} \mu_{\mathrm{g}}=\frac{\lambda_{\mathrm{w}}}{\lambda_{\mathrm{g}}}=\frac{5}{4} \\
& \frac{\mu_{\mathrm{g}}}{\mu_{\mathrm{w}}}=\frac{5}{4} \\
& \mu_{\mathrm{w}}=\frac{4}{5} \mu_{\mathrm{g}}=\frac{4}{5} \times \frac{5}{3}=\frac{4}{3}=1.33
\end{aligned}$
$\begin{aligned}
& \lambda_{\mathrm{w}}=\frac{5}{\mathrm{~N}}, \quad \lambda_{\mathrm{g}}=\frac{4}{\mathrm{n}} \\
& { }_{\mathrm{w}} \mu_{\mathrm{g}}=\frac{\lambda_{\mathrm{w}}}{\lambda_{\mathrm{g}}}=\frac{5}{4} \\
& \frac{\mu_{\mathrm{g}}}{\mu_{\mathrm{w}}}=\frac{5}{4} \\
& \mu_{\mathrm{w}}=\frac{4}{5} \mu_{\mathrm{g}}=\frac{4}{5} \times \frac{5}{3}=\frac{4}{3}=1.33
\end{aligned}$
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