Three immiscible liquids of densities `d_1 gt d_2 gt d_3` and refractive indices `mu_1 gt mu_2 gt mu_3` are put in a beaker. The height of each liquid column is `(h)/(3)`. A dot is made at the bottom of the beaker. For near normal vision, find the apparent depth of the dot.

Explanation

Here, real depth of the ot under liquid of density `d_1` is `h//3`. If `x_1` is its apparent depth, when seen from air then from `mu_1 = (h//3)/(x_1)` or `x_1 = (h)/(3 mu_1)`
Similarly, apparent depths of the dot when seen from air through two other liquids are
`x_2 = (h)/(3 mu_2)` and `x_3 = (h)/(3 mu_3)`
`:.` Apparent depth of the dot seen from air through the three liquids is
`x = x_1 + x_2 + x_3 = (h)/(3 mu_1)+(h)/(3 mu_2)+(h)/(3 mu_3)=(h)/(3) [(1)/(mu_1)+(1)/(mu_2)+(1)/(mu_3)]`.