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

(a) `5/2` , (b) `sqrt((5)/(2))` , (c) `sqrt((3)/(2))` , (d) `(3)/(2)`

Explanation

`PQ =QR =2h`
` therefore (2525) i=45^@`
`therefore ST =RT =h=KM=MN`
so` KS= sqrt(h^2 +(2h)^2)=hsqrt(5)`
` therefore sin r = (h)/(h sqrt(5))=(1)/(sqrt(5))`
` therefore mu = (sin i)/( sin r ) = ( sin 45^@ )/( 1//sqrt(5))=sqrt((5)/(2))`