Problem 3

A thin converging lens has focal length

f>0

. A planar object perpendicular to the principal axis is placed a distance

3f

from the lens. Using the thin-lens model and the convention that real images have positive image distance, find the signed image distance

v

, lateral magnification

m

, and describe the image. Use the stated signed-distance convention and assume a sufficiently small object so the paraxial approximation applies. (a) Determine the image position from the conjugate equation. (b) Calculate the magnification and image height if the object height is

H

. (c) Decide whether the image is real or virtual and upright or inverted, and check the dimensional consistency.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

u=3f,\qquad \frac{1}{f}=\frac{1}{u}+\frac{1}{v}

problems.proof.analysis

The object distance is $u=3f$ . With real image distance positive, the thin-lens equation is $1/f=1/u+1/v$ .