Problem 3

A transverse object of height

H

is placed before a converging thin lens of focal length

f>0

, perpendicular to its principal axis. Its distance from the lens is

u=3f

; use the convention that image distance

v>0

lies opposite the object and signed transverse magnification is

M=-v/u

. (a) Use the principal-ray construction to determine the image character and location. (b) Find the signed magnification and image height. (c) If a smaller object is placed at the same position, state what changes and what does not, explaining with the lens equation.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

v=\frac{uf}{u-f},\qquad M=-\frac{f}{u-f}

problems.proof.analysis

Solving the lens equation for fixed $u$ shows that $v$ depends only on $u$ and $f$ , not on $H$ . With $u,f$ unchanged, magnification is unchanged while image size scales with object height.