An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is

Options

A. `(5)/(2)`
B. `sqrt((5)/(2))`
C. `sqrt((3)/(2))`
D. `(3)/(2)`

Answer

B

Explanation

Obviously , as `i=45^(@)`

and `sinr = h//AC = h//h sqrt(5) = (1)/(sqrt(5))`,
`mu = (sin i)/(sinr) = (1//sqrt(2))/(1//sqrt(5)) = sqrt((5)/(2))`