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) → \( \left(1-\displaystyle\frac{1}{\mu_{w}}\right)h_1+\left(1-\displaystyle\frac{1}{\mu_{k}}\right)h_2 \)
Seen from above (near-normal viewing), a layer of thickness h and refractive index \( \mu \) makes the object below it appear raised by the apparent shift \( h\left(1-\frac{1}{\mu}\right) \). The two layers each cause their own shift, and the shifts add.
\( \displaystyle \Delta_{\mathrm{water}} = h_1\left(1-\frac{1}{\mu_w}\right),\qquad \Delta_{\mathrm{oil}} = h_2\left(1-\frac{1}{\mu_k}\right) \)
\( \displaystyle \Delta = \left(1-\frac{1}{\mu_w}\right)h_1 + \left(1-\frac{1}{\mu_k}\right)h_2 \)