Answer to Question #128149 in Optics for Aadhavan

Question

A short linear objectbof height b lies along the axis of a concave mirror that has a focal length of f and at a distance b from the pole of mirror. What is the height of the image?

Answer 1

According to the mirror formula;

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\to(i)$

After differentiation we get;

$\implies-v^{-2}dv-u^{-2}du=0$

or it can be $|dv|=|\frac{v^2}{u^2}|du\to(ii)$

$|dv|=$ size of the image

$|du|=$ size of the object $(=b)$

From the equation ($i$ ) above rewrite as;

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

When we square both sides we find that;

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

When we substitute in equation ( $ii$ ) we find that the size of the image is;

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