A point source of light is placed at the bottom of a vessel which is filled with water of refractive index `mu` to a height h. If a floating opaque disc has to be placed exactly above it so that the source is invisible from above, the radius of the disc should be-

Options

A. `(h)/(sqrt(mu - 1))`
B. `(h)/(sqrt(mu^(2) - 1))`
C. `(h)/(mu^(2) - 1)`
D. `(mu h)/(sqrt(mu^(2) - 1))`

Answer

B

Explanation

r should be such that rays beyond it got totally internally reflected for this `theta gt ` C or `sin theta gt ` sin C

Also `mu = (1)/(sin C ) therefore (r )/(sqrt(h^(2) + r^(2)) ) gt (1)/(mu)`
In limiting case ` (r )/(sqrt(h^(2) + r^(2)) ) = (1)/(mu)`
Solving we get r = `(h)/(sqrt(mu^(2)- 1))`