A rod of height h is palced in a beaker of same radius. The height of the beaker is 3 times its radius. An observer sees the top end of the rod through a pin hole. When the beaker is filled with a liquid of refractive index `sqrt(mu)` upto a height 2h, he can see the lower end of the rod. Find the value of `mu`

Answer

`2.5`

Explanation

The line of sight of the observer remains constant, making an angle of `45^(@)` with the normal
`sin theta=h/(sqrt(h^(2)+(2h)^(2)))`
`=1/(sqrt(5))`
Refractive index of liquid
`sqrt(mu)=(sin 45^(@))/(sin theta)`
`=(1/(sqrt(2)))/(1/(sqrt(5)))=sqrt((5/2))`
`:.sqrt(mu)=sqrt(2.5)impliesmu=2.5`