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

Answer

C

Explanation

Follow the figure, let fish is located at `O`
Critical angle, `sin theta_(C)=(1)/(mu)`
Also, `tantheta_(C)=(AB)/(AO)impliesAB=OA tan theta_(C)`
or `AB=(OA)/(sqrt(mu^(2)-1))=(12)/(sqrt(((4)/(3))^(2)-1))=(36)/(sqrt(7))`