MHT CET · Physics · Ray Optics
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
- A 1.33
- B 1.3
- C 1.25
- D 1.1
Answer & Solution
Correct Answer
(A) 1.33
Step-by-step Solution
Detailed explanation
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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