Question

A short linear object of length $L$ lies on the axis of a spherical mirror of focal length $f$ at a distance $u$ from the mirror. Its image has an axial length $L$ equal to :

• A. $L{\left[\frac{f}{(u-f)}\right]}^{1/2}$
• B. $L{\left[\frac{u+f}{\left(f\right)}\right]}^{1/2}$
• C. $L{\left[\frac{u+f}{\left(f\right)}\right]}^2$
• D. $L{\left[\frac{f}{(u-f)}\right]}^2$

Answer 1

The correct option is D $L{\left[\frac{f}{(u-f)}\right]}^2$

From mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

On differentiating, we get

$\frac{-dv}{v^2}-\frac{du}{u^2}=0\therefore dv=-du{\left(\frac{v}{u}\right)}^{2}as\frac{v}{u}=\frac{f}{u-f}\therefore dv=-du{\left[\frac{f}{u-f}\right]}^2{L}^{\prime }=L{\left[\frac{f}{u-f}\right]}^2$