Problem 3

A small upright object of height

h

is placed perpendicular to the principal axis of a thin converging lens, at distance

u=3/2f

from its optical centre; the focal length is

f>0

and

u>f

. The media on both sides are the same. Use

u>0

, take a real image on the opposite side to have

v>0

, and define signed magnification by

m=-v/u

. (a) Find the image distance

v

in terms of

f

. (b) Find the magnification and image height, and state whether the image is real or virtual and upright or inverted. (c) If the object is moved a small distance farther from the lens, determine the image’s direction of motion from the dependence of

v

u

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

du>0\Longrightarrow dv<0: \text{image moves toward the lens}

problems.proof.analysis

The derivative $dv/du=-f^2/(u-f)^2$ is always negative. Increasing $u$ therefore decreases $v$ : the real image moves toward the lens, not farther away with the object.