A glass beaker contains water upto a height $h_1$ and kerosene oil above water upto height $h_2$. If the refractive index of water is $\mu_{w}$ and that of oil is $\mu_{k}$, then what will be the apparent shift in the position of the bottom of the beaker when viewed from above?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\left(1-\frac{1}{\mu_{w}}\right) h_1+\left(1-\frac{1}{\mu_{k}}\right) h_2$
The apparent shift (Δh) due to a layer of thickness h and the refractive index (μ) is -
$Δh=h\left(1-\frac{1}{μ}\right)$
$∴Δh_{total}=Δh_{water}+Δh_{oil}$
$=h_1\left(1-\frac{1}{μ_w}\right)+h_2\left(1-\frac{1}{μ_k}\right)$