Question

Two lenses are placed along the x axis, with a diverging lens of focal length −7.40 cm on the left and a converging lens of focal length 15.0 cm on the right. When an object is placed 14.0 cm to the left of the diverging lens, what should the separation s of the two lenses be if the final image is to be focused at x = ∞?

Answer 1

for the final image to be focused at infinity,the image from the diverging lens should form at a distnace equal to focal length of the converging lens=15 cm

Given focal length of diverging lens=f=-7.4 cm

object distance of the object from diverging lens=u=14 cm

Let the image distnace be v

Per lens formula,

1/f=1/u+1/v

1/-7.4=1/14+1/v

v=-4.84 cm

negative value of v means the image is formed at the object side of the diverging lens

let the separation between the converging and diverging lens be s

s+4.84=15

s=10.159 cm

Therefore, the separation should be 10.159 cm