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 , let `OS = h` be the max. height of liquid above the source for which the source cannot be seen at all.
`:. /_OSA = C`
Any other ray from `S` will be totally internally reflected because in that case, angle of incidence will be greater them the critical angle.
In `Delta OSA, sin C = (OA)/(SA) = (r)/(sqrt(r^2 + h^2)) = (1)/(mu)`
or `(1)/(mu^2) = (r^2)/(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`.
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