Problem 3

A thin converging lens of focal length

f=20

cm stands in air. A small luminous object of height

H=2.0

cm is perpendicular to the principal axis,

u=30

cm in front of the lens. Use the convention that a real image has

v>0

, the lens equation

1/f=1/u+1/v

, and lateral magnification

m=-v/u

. (a) Find the image distance and height. (b) State whether the image is real or virtual and upright or inverted. (c) The object is moved farther away to

u=60

cm; find the new image and describe the size change.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\frac1{30}+\frac1{60}=\frac3{60}=\frac1{20}\checkmark,\qquad \frac1{60}+\frac1{30}=\frac1{20}\checkmark

problems.proof.analysis

Substitute both $(u,v)$ pairs back into the lens formula. Each gives $1/f=1/20$ cm $^{-1}$ , matching the stated $f=20$ cm, so the results are consistent.