Question

A point source of light is placed at a depth of h below the surface of water of refractive index `mu`. A floating opaque disc is placed on the surface of water so that light from the source is not visible from the surface. The minimum diameter of the disc is
A. `(2h)/((mu^(2) - 1)^(1//2))`
B. `2h(mu^(2)-1)^(1//2)`
C. `(h)/(2(mu^(2)-1)^(1//2))`
D. `h(mu^(2)-1)^(1//2)`

Answer 1

Correct Answer - A
The figure shows incidence from water at critical angale `theta_(c)` for the limiting case.
Now, `sin theta_(c) = 1/mu`
so that `tantheta_(c) = (1)/((mu^(2)-1)^(1//2))`
From figure, `tantheta_(c) = (r)/(h)`
where r is the radius of the disc.
`:.` Dismeter of the disc `2r = 2h tan theta_(c) = (2h)/((mu^(2)-1)^(1//2))`