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

Let d be the diameter of the disc. The spot shall be invisible if the incident rays from the dot at O to the surface at d/2 at the criticale angle.
Let `i` be the angle of inidence
Using releatioship between refractive index and critical angle
then, `" " sint =(1)/(mu)` ltbr Unsing geometry and trigonometry
Now `" " (d//2)/(h)=tani`
`rArr " " (d)/(2)=h tan i=h"["sqrt(mu^(2)-1)"]"^(-1)`
`:. " " d=(2h)/(sqrt(mu^(2)-1))`
This is the required expression of d.