A monochromatic ray of light travels through glass slab and water column. The number of waves in glass slab…
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 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
$\frac{4}{3}$
$\frac{5}{4}$
$\frac{6}{5}$
$\frac{3}{2}$
Solution
Given thickness of glass slab $=4 \mathrm{~cm}$ and height of water column $=5 \mathrm{~cm}$
and refractive index of glass $\mu_g=\frac{5}{3}$
As number of waves is equal in both the glass and water medium, then according to their height and thickness, we can write
$\begin{aligned} & \frac{\mu_w}{\mu_g}=\frac{v_g}{v_w}=\frac{\frac{\text { thickness of glass }}{\text { time }}}{\frac{\text { height of water column }}{\text { time }}} \\ & \Rightarrow \frac{\mu_w}{\mu_g}=\frac{4}{5} \\ & \Rightarrow \mu_w=\frac{4}{5} \times\left(\frac{5}{3}\right)=\frac{4}{3}\end{aligned}$
/