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

1/v=1/60\,\mathrm{cm}^{-1}\Rightarrow v=60\,\mathrm{cm}

problems.proof.analysis

This equation expresses the physical law governing the system. It incorporates the stated constraint rather than treating the relevant quantities as independent.

problems.proof.pitfall. Check the sign convention and physical case carefully; do not use a formula for a different motion or geometry.