Question

A short liner object, of length $l$, lies along the axis of a concave mirror, of focal length $f$, at a distance d from the pole of the mirror. The size of the image is then (nearly):

• A. $\frac{lf}{d-f}$
• B. $\frac{d-f}{If}$
• C. $l\frac{f^2}{{(d-f)}^2}$
• D. $\frac{(d-f{)}^2}{f^2}l$

Answer 1

Answer: (C)

$l\frac{f^2}{{(d-f)}^2}$

From mirror equation,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$⟹\left|dv\right|=\left|\frac{v^2}{u^2}\right|\left|du\right|$

$\left|dv\right|$ is the size of image

$\left|du\right|$ is the size of object

From the equation

$\frac{v^2}{u^2}=\frac{v^2}{d^2}=(\frac{f}{d-f}{)}^2$
Thus size of the image is $l\frac{f^2}{(d-f{)}^2}$