Problem 3

On an optical bench, a thin converging lens of focal length

f=10.0\,\mathrm{cm}

is used with an object of height

h_o=2.00\,\mathrm{cm}

placed on the principal axis, initially at distance

u=30.0\,\mathrm{cm}

. Work in air and in the paraxial approximation. For a real object take

u>0

; a real image has

v>0

. Define transverse magnification by

M=h_i/h_o=-v/u

. (a) Find the image distance and magnification, and state whether the image is real or virtual and upright or inverted. (b) Find the image height. (c) Move the object to

u=15.0\,\mathrm{cm}

and repeat the position, magnification, and image-character determination, then compare the two placements.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\boxed{(u=30\,\mathrm{cm}):v=15\,\mathrm{cm},M=-0.5,h_i=-1\,\mathrm{cm};\quad(u=15\,\mathrm{cm}):v=30\,\mathrm{cm},M=-2,h_i=-4\,\mathrm{cm}}

problems.proof.analysis

Both placements produce real, inverted images; moving the object toward the focal point sends the image farther away and increases magnification. The signs of $v$ and $M$ agree with the stated convention.