Question

A jar of height h is filled wih a transparent liquid of refractive index `mu`, Fig. At the centre of the jar on the botom surface is a dot. Find the minimum diameter of a disc, such that when placed on the top surface symmetrically about the centre, the dot is invisible.
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Answer 1

In Fig. `O` is a on dot the bottom surface of a jar of height `h`, filled with a transparent liquid of refraactive index `mu`. `AB = d` is diameter of a disc such that when placed on the top surface, symmetrically about the centre, the dot is invisible. This would happen when rays `OA and OB` suffer total internal reflection.
If `angle AOC = i`,
then `tan i = (AC)/(OC) = (d//2)/(h)` ...(i) For total internal reflection, `i ge c`,
when `sin i = sin c = (1)/(mu) and tan i = (1)/(sqrt(mu^(2) - 1))`, Fig. ...(ii)
From (i) and (ii), `(d)/(2h) = (1)/(sqrt(mu^(2) - 1))`
`d = (2h)/(sqrt(mu -1))`