Physics - Geometrical Optics Question with Solution | TestHub

The problem involves calculating the apparent shift in the position of the bottom of a beaker when viewed from above, considering two layers of different refractive indices (water and kerosene).

The apparent shift due to each layer can be calculated separately, and then the total shift is the sum of the individual shifts. The formula for the apparent depth ($d^{\prime }$) when viewing an object at a real depth ($d$) through a medium of refractive index $\mu$ is given by:

$d^{\prime }=\frac{d}{\mu }$

The apparent shift is the difference between the real depth and the apparent depth:

Shift = $d-d^{\prime }=d-\frac{d}{\mu }=d(1-\frac{1}{\mu })$

For the water layer of height $h_1$ and refractive index ${\mu }_1$, the apparent shift is:

$S_1=h_1(1-\frac{1}{{\mu }_1})$

For the kerosene layer of height $h_2$ and refractive index ${\mu }_2$, the apparent shift is:

$S_2=h_2(1-\frac{1}{{\mu }_2})$

The total apparent shift (S) is the sum of the shifts due to both layers:

$S=S_1+S_2=h_1(1-\frac{1}{{\mu }_1})+h_2(1-\frac{1}{{\mu }_2})$

Therefore, the total apparent shift is:

$S=(1-\frac{1}{{\mu }_1})h_1+(1-\frac{1}{{\mu }_2})h_2$

Comparing this result with the given options, option B matches our derived expression.

Therefore, the correct answer is B.