A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is `(4)/(3)` and the fish is 12 cm below the surface, the radius of this circle is cm is

Options

A. `4 sqrt5`
B. `36 sqrt5`
C. `(36)/(sqrt7)`
D. `36 sqrt7`

Answer

C

Explanation

Let r be the radius of the circular horizon , through which the fish sees the outside world .

The ray OQ is the incident at the critical angle , so that `sin i_(c) = (1)/(n) = (3)/(4) and tan i_(c) = (r)/(Po) = (r)/(12)`
`therefore r = 12 tan i_(c) = 12 xx (3)/(sqrt7) = (36)/(sqrt7)`

`sin i_(c) = (3)/(4)`
`tan i_(c) = (3)/(sqrt7)`