A thin convex lens of refractive index `mu=1.5 ` is placed between a point source of Light S and a screen A, shown in figure,. Light rays from the source S are brought to focus on the screen A, forming a point image P. The distance SP is equal to 50cm. Water `(mu=4//3)` is now poured into a vessel interposed between the object and the lens, and it is observed that when the water level is 8cm the screen has to be moved up by a distance of 6cm in order to get a sharp image. Find the focal length of the lens.

Answer

`|u|=20cm`
`|v|=30cm ` and `f=12cm`

Explanation

Suppose that the object distance (between the oject and the lens) be u and the image distance v. Then,
`|u|+|v|=50`
`(1)/(|v|)-(1)/(|u|)=(1)/(f)` (i)
When water is poured into the vessel,
`(1)/((|v|+6))-(1)/(-(|u|-2))=(1)/(f)` (ii)
Solving the equation, we get
`|u|=20cm`
`|v|=30cm` and `f=12cm`