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

Let us consider that `h_(1)` is the apparent depth of the dot when viewed from air through first liquid of refractive index `mu_(1)`.
`"Then, "mu_(1)=(h//3)/(h_(1))`
`rArr" "h_(1)=(h)/(3mu_(1))`
The apparent depth of the dot viewed from air through other two liquids is
`h_(2)=(h)/(3mu_(2)) and h_(3)=(h)/(3mu_(3))`
The total apparent depth of the dot viewed from outside through the three liquid is
`h=h_(1)+h_(2)+h_(3)`
`=(h)/(3)[(1)/(mu_(1))+(1)/(mu_(2))+(1)/(mu_(3))]`