Question

An observer can see the top end B of a thin rod of height h through a pin-hole. The height of the beaker is 3h, and the radius is h. When the beaker is filled with a liquid up to a height of 2h, the observer can see the lower end A of the rod. The refractive index of the liquid is:

Options

• `5/2`

• `sqrt(5/2)`

• `sqrt(3/2)`

• `3/2`

Answer 1

`sqrt(5/2)`

Explanation:

In figure,

AC = `sqrt((2h)^2 + h^2)`

= `hsqrt5`

BC = `sqrt(h^2 + h^2)`

= `hsqrt2`

The ray AC incident on the water surface at ∠r is refracted along CD. If μ is refractive index of water, then from Snell’s law,

μ = `(sin (90 - i))/(sin r)`

= `(cos i)/(sin r)`

= `((BD)/(BC))/((AE)/(AC))`

= `(AC)/(BC)`

= `(hsqrt5)/(hsqrt2)`

= `sqrt(5/2)`