First slide

Ray optics

Question

A short linear object of length b lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror, what is the size of image?

Moderate

A

$(\frac{f}{u - f}) b^{2}$
B

${(\frac{f}{u - f})}^{2} b$
C

$(\frac{f}{u + f}) b^{2}$
D

${(\frac{2 f}{u - f})}^{2} b$

Solution

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$1 + \frac{1}{m} = \frac{u}{f}$
$\frac{1}{m} = \frac{u}{f} - 1 = \frac{u - f}{f} m = \frac{f}{u - f} = \frac{v}{u}$
$\frac{- dv}{v^{2}} - \frac{du}{u^{2}} = 0$
$\frac{du}{u^{2}} = \frac{dv}{v^{2}}$
$dv = \frac{v^{2}}{u^{2}} du = {(\frac{f}{u - f})}^{2} b$

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