Problem 3

A small upright object of height

h

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

u=3f

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

\boxed{v=\frac{3}{3-1}f,\quad m=-\frac1{3-1},\quad |h'|=\frac{h}{3-1};\text{ real, inverted}}

problems.proof.analysis

Collect all requested quantities and retain the sign of $m$ to distinguish orientation from size. Dimensions are consistent: $v,f,u$ are lengths, $m$ is dimensionless, and $mh$ is a length.