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.