A vessel of depth $$d$$ is half filled with oil of refractive index $$n_1$$ and the other half is filled with water of refractive index $$n_2$$. The apparent depth of this vessel when viewed from above will be-

Find the apparent depth of a vessel of depth $$d$$ half filled with oil (refractive index $$n_1$$) and half filled with water (refractive index $$n_2$$).

For a layer of real depth $$t$$ and refractive index $$n$$, the apparent depth is $$\frac{t}{n}$$. Each layer here has real depth $$\frac{d}{2}$$, so the apparent depth of the oil layer is $$\frac{d/2}{n_1}$$ and that of the water layer is $$\frac{d/2}{n_2}$$. Adding these, the total apparent depth becomes $$\frac{d}{2n_1} + \frac{d}{2n_2} = \frac{d}{2}\left(\frac{1}{n_1} + \frac{1}{n_2}\right) = \frac{d}{2}\cdot\frac{n_1 + n_2}{n_1 n_2} = \frac{d(n_1 + n_2)}{2n_1 n_2}$$.

The correct answer is Option B: $$\frac{d(n_1 + n_2)}{2n_1 n_2}$$.