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 water surface, the radius of this circle (in cm) is .....

Options

A. `36root_2`
B. `4root_5`
C. `36root_7`
D. `(36)/(root_7)`

Answer

C, D

Explanation

`sinC=(R)/(sqrt(R^2+D^2))`
`1/n=(R)/(sqrt(R^2+D^2))`
`(1)/(n^2)=(R^2)/(R^2+D^2)`
`thereforeR^2+D^2=n^2R^2`
`thereforeD^2=R^2(n^2-1)`
`therefore(D^2)/(n^2-1)=R^2`
`thereforeR=(D)/(sqrt(n^2-1))`
`thereforeR=(12)/(sqrt((4/3)^2)-1)=(12)/(sqrt((16)/(9)-1))`
`thereforeR=(36)/(sqrt7)` cm