Question

When an object is at distance of ${\mu }_1$ and ${\mu }_2$ from the poles of a convex mirror, image of the same size are formed. The focal length of the mirror is:

• A. $|u_1+u_2|$
• B. $|u_1-u_2|$
• C. $\left|\frac{u_1+u_2}{2}\right|$
• D. $\left|\frac{u_1-u_2}{2}\right|$

Answer 1

The correct option is C $\left|\frac{u_1+u_2}{2}\right|$

$\begin{array}{c}\frac{1}{v}=\frac{1}{f}-\frac{1}{u}\\ \Rightarrow \frac{u}{v}=\frac{u}{f}-1\\ \left|\frac{{\mu }_1}{v_1}\right|=\left|\frac{{\mu }_1}{f}-1\right|=\left|\frac{{\mu }_2}{f}-1\right|\\ \Rightarrow \frac{{\mu }_1}{f}+1=-\frac{{\mu }_2}{f}+1\\ \Rightarrow \left|{\mu }_1+{\mu }_2\right|\frac{1}{f}=2\\ \Rightarrow f=\frac{\left|{\mu }_1+{\mu }_2\right|}{2}\\ \therefore Ans.\left(C\right)\end{array}$