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. `36 sqrt(7)`
B. `(36)/(sqrt(7))`
C. `36 sqrt(5)`
D. `4 sqrt(5)`

Answer

B

Explanation

(b) The situtaion is shown in figure.
`sin theta_(C ) = (1)/(mu)` hence `tan theta_(C ) = (AB)/(AO)` `:. AB = OA tan theta_(C )`
or `AB = (OA)/(sqrt(mu^(2) -1)) = (12)/(sqrt(((4)/(3))^(2) - 1)) = (36)/(sqrt7)`