MHT CET · Physics · Ray Optics
When the same monochromatic ray of light travels through glass slab and through water, the number of waves in glass slab of thickness 5 cm is same as in water column of height 6 cm . If refractive index of glass is 1.56 , then refractive index of water is
- A 1.28
- B 1.29
- C 1.3
- D 1.32
Answer & Solution
Correct Answer
(C) 1.3
Step-by-step Solution
Detailed explanation
Given: \(\mathrm{N}_{\mathrm{g}}=\mathrm{N}_{\mathrm{w}}\)
But number of waves \(N=\frac{d}{\lambda}\);
where \(\mathrm{d}=\) thickness of the medium
\(\begin{array}{ll}
\therefore & \frac{d_g}{\lambda_g}=\frac{d_w}{\lambda_w} \\
& \text { But } \lambda_{\mathrm{g}}=\frac{\lambda_{\text {air }}}{\mu_{\mathrm{g}}} \text { and } \lambda_w=\frac{\lambda_{\text {air }}}{\mu_w} \\
\therefore \quad & \mu_{\mathrm{g}} d_g=\mu_{\mathrm{w}} d_w \\
\therefore & \mu_{\mathrm{w}}=\frac{\mu_{\mathrm{g}} d_g}{d_w}=\frac{1.56 \times 5}{6}=1.30
\end{array}\)
But number of waves \(N=\frac{d}{\lambda}\);
where \(\mathrm{d}=\) thickness of the medium
\(\begin{array}{ll}
\therefore & \frac{d_g}{\lambda_g}=\frac{d_w}{\lambda_w} \\
& \text { But } \lambda_{\mathrm{g}}=\frac{\lambda_{\text {air }}}{\mu_{\mathrm{g}}} \text { and } \lambda_w=\frac{\lambda_{\text {air }}}{\mu_w} \\
\therefore \quad & \mu_{\mathrm{g}} d_g=\mu_{\mathrm{w}} d_w \\
\therefore & \mu_{\mathrm{w}}=\frac{\mu_{\mathrm{g}} d_g}{d_w}=\frac{1.56 \times 5}{6}=1.30
\end{array}\)
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