An object is placed at a distant of `1.50` from a screen and a convex lens placed in between produces an image magnified `4` times on the screen .What is the focal length and the position of the lens.

Explanation

`m = (h_(2))/( h_(1)) =- 4 `

Then `u = - x ` and `v= (1.5 - x)`
using `m = (v )/( u )` we get `-4 = (1.5 - x)/( - x)`
`rArr x= 0.3 ` metre
The lens is placed at a distance of 0.3 m from the object (or 1.20 m from the screen ) for focal length we may use
`m = ( f)/( f + u)` or `-4 = ( f ) /( f+ (-0.3))`
`rArr f = (1.2)/(5 ) = 0.24 cm`