The refractive index of a glass plate is $\frac{3}{2}$. Then, the correct thickness of glass plate that will permit the same number of wavelengths as that by an $18\text{cm}$ long column of water $(\mu =\frac{4}{3})$ will be

The correct option is B $16\text{cm}$
Let the wavelength of light be ${\lambda }_w$ in water and the total number of wavelengths be $n$.
Then, $n{\lambda }_w=18$ ...............$\left(1\right)$
Similarly,
Let the wavelength of light be ${\lambda }_g$ in glass plate and the total number of wavelengths be $n$ $($same as in water$)$.
Then, $n{\lambda }_g=t$ ...............$\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$,
$\frac{{\lambda }_w}{{\lambda }_g}=\frac{18}{t}$ ...............$\left(3\right)$
We know that, relative refractive index,
${}_g{\mu }_w=\frac{{\mu }_g}{{\mu }_w}=\frac{{\lambda }_w}{{\lambda }_g}$
$\Rightarrow \frac{3/2}{4/3}=\frac{18}{t}$
$[$from $\left(3\right)]$
$\Rightarrow t=16\text{cm}$

Why this question? Tips: Here, the thickness of the medium will be an integral multiple of the wavelength of light.