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

(Hint : the image formed by first medium act as an object for second medium) Let the apparent depth be `O_1` for the object seen from `O_1 =mu_2/mu_1 h/3` image formed by medium 1, O acts as an object for medium 2. It is seen from `M_3`, the apparent depth is `O_2`. Similarly, the image found by medium 2, `O_2` act as an object for medium 3
`O_2=mu_3/mu_2(h/3+O_1)`
`O_3=mu_3(h/3 + O_2)` putting value of `O_2 and O_1`
`O_3=h/3(1/mu_1+1/mu_3+1/mu_3)`