On a bright sunny day a diver of height h stands at the bottom of a lake of depth H. Looking upward, he can see objects outside the lake in a circular region of radius R. Beyond this circle he sees the image of objects lying on the floor of the lake. If refractive index of water is 4/3, then the value of R is–

Options

A. `(3(H-h))/(sqrt(7))`
B. 3h `sqrt(7)`
C. `(H-h)/(sqrt((7)/(3)))`
D. `((H-h))/(sqrt((5)/(3)))`

Answer

A

Explanation

`n_(2) sin C = n_(1) sin 90`
`(4)/(3) sin C = 1 rArr sin C - (3)/(4) `
`tanC = (3)/(sqrt(7)) = (R )/(H - h)`
`R = (3)/(sqrt(7)) (H - h).`