The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall `3 m` away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose ?

Explanation

Let a large convex lens is placed between two walls at a distance x from wall on which an electric bulb is fixed.

Using lens formula,`1/f=1/v-1/u`
Putting,u=x and v=4-x
`1/f=1/(4-x)-1/(-x)`
or `1/f=(x+4-x)/((4-x)(x))or1/f=4/((4-x)(x))`
or `f=((4-x)x)/4`
Now, magnification, m`=v/u=(4-x)/xor1=(4-x)/x`
or x=4-xor2x=4or x=2m
From Eq. (i) we get
`f=((4-2)(2))/4=(2xx2)/4=1m`