Problem 3

A thin converging lens in air has focal length

f=20\,\mathrm{cm}

, and a real upright object of height

H=2.0\,\mathrm{cm}

is placed

u=30\,\mathrm{cm}

in front of it. Use the Cartesian convention in which a real object has positive

u

and a real image has positive

v

, so

1/f=1/u+1/v

; neglect lens thickness. (a) Find the image distance

v

. (b) Determine whether the image is real or virtual and upright or inverted. (c) Find its signed magnification and height.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

v>0\Rightarrow\text{real},\quad m<0\Rightarrow\text{inverted}

problems.proof.analysis

Finally substitute the given values and check units and limiting behavior. The result agrees with the signs and scale implied by the model and previous parts.