Problem 3

An object is placed a distance

u>f

from a converging thin lens of focal length

f>0

. Use the thin-lens convention

1/f=1/u+1/v

, with a real image having

v>0

. Find the image position and signed lateral magnification

M

for object height $h. Assume the string, pulley, electrical source, or optical apparatus is ideal as stated, and neglect any effect not specified. State a clear sign convention, identify the physical Keep one model and sign convention throughout. Reuse each intermediate result with the same convention, then check that the answer has the required physical dimensions. (a) Set up the physical relation. (b) Find an intermediate quantity. (c) Obtain the answer and check its conditions and units.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\boxed{v=\frac{fu}{u-f}},\quad \boxed{M=-\frac f{u-f}},\quad \boxed{h_i=-\frac{fh}{u-f}}

problems.proof.analysis

As $u$ tends to infinity, $v$ tends to $f$ and the image height tends to zero, consistent with the geometry. This is consistent with the stated model and the chosen sign convention.