A converging lens and a diverging mirror are placed at a separation of 15 cm. The focal length of the lens is 25 cm and that of the mirror is 40 cm. Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis ?

Explanation

image by mirror:
`u=-d,f'=40cm,v=?`
`(1)/(v)+(1)/(u)=(1)/(f')implies(1)/(v)+(1)/(-d)=(1)/(40)implies(1)/(v)=(1)/(40)+(1)/(d)=(d+40)/(40d)`
`v=(40d)/(d+40)`
Image of `O` is formed at `I_(1)`
Since final beam is parallel to principal axis, for this image by mirror should be formed at focus of the lens.
`15+(40d)/(d+40)=25`
`(40d)/(d+40)=10impliesd=(40)/(3)`cm