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

sin `theta = (h)/(sqrt(h^(2) + (2h)^(2) ) ) = (1)/(sqrt(5)) `
Snell.s law,
`sin 45^(@) = n sin theta`
`rArr " " n = (1// sqrt(2))/(1 // sqrt(5)) = sqrt(5//2)`.