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

m=-30/60=-0.50,\quad h'=-1.0\ \mathrm{cm};\quad (u=30): (v,h')=(60\ \mathrm{cm},-4.0\ \mathrm{cm});\quad (u=60): (v,h')=(30\ \mathrm{cm},-1.0\ \mathrm{cm})

problems.proof.analysis

At $u=60$ cm the image height is $mH=-1.0$ cm: still inverted, but half the object height. Answers: first case, real and inverted with $v=60$ cm and $|h'|=4.0$ cm; second case, $v=30$ cm and $|h'|=1.0$ cm.