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

For the image of point P to be seen by the observer, it should be formed at point Q. In triangleQNS,
`NS=QS=2h`
:'`angle NQS=45degree`
'r=45degree`
Now in `triangleQMA`,`angleMQA=45degree`
,' `MA=QA=h`
`_2^1mu=(sinr)/(sini)=(sin45degree)/(sini)`
In PMB,
`PM^2=4h^2+h^2=5h^2`
:' `sini=(h)/(sqrt5h)=(1)/(sqrt5)`
From(i)and(ii)
`_2^1mu=sqrt((5)/(2))`
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