Question

A point source of light `S` is placed at the bottom of a vessel containing a liquid of refractive index `5//3`. A person is viewing the source from above the surface. There is an opaque disc of radius `1 cm` floating on the surface. The centre of disc lies vertically above the source `O`. The liquid from the vessel is gradually drained out through a tap. What is the maximum height of the liquid for which the source cannot be seen at all.

Answer 1

In Fig., let `OS = h` be the max. height of liquid above the source for which the source cannot be seen at all.

`:. angle OSA = C`
Any other ray from S will be totally internally refracted because in that case, angle of incidence will be greater them the critical angle.
In `DeltaOSA, sin C = (OA)/(SA) = (r )/(sqrt(r^(2) + h^(2))) = (1)/(mu)`
or `(1)/(mu_(2)) = (r )/(r^(2) + h^(2))`
`r^(2) + h^(2) = mu^(2) r^(2)`
`h^(2) = r^(2)(mu^(2) - 1)`
`h = r sqrt(mu^(2) - 1) = 1 sqrt((5//3)^(2) - 1`
`h = (4)/(3) = 1.33 cm`