Question

$0.04m$ of glass contains the same number of waves as $0.05m$ of water, when monochromatic light passes through them normally. Refractive index of water is $4/3$. Refractive index of glass is

• A. $5/3$
• B. $5/4$
• C. $5/6$
• D. $4/5$

Answer 1

The correct option is A $5/3$

Let the number of waves in glass and water be $n$

Then, wavelength of the light in glass is ${\lambda }_{\text{glass}}=0.04/n$

and wavelength of the light in water is ${\lambda }_{\text{water}}=0.05/n$

Let $\omega$ be the frequency of the monochromatic light.

Thus, speed of light in glass is $c_{\text{glass}}={\lambda }_{\text{glass}}\times \omega =0.04\omega /n$

and speed of light in water is $c_{\text{water}}={\lambda }_{\text{water}}\times \omega =0.05\omega /n$

Relative refractive index is $\frac{{\mu }_{\text{water}}}{{\mu }_{\text{glass}}}=\frac{c_{\text{glass}}}{c_{\text{water}}}=\frac{4}{5}$

Given ${\mu }_{\text{water}}=4/3\Rightarrow {\mu }_{\text{glass}}=4/3\times 5/4=5/3$