Question

A convex mirror of focal length f forms an image which is $\frac{1}{n}$ times the object. The distance of the object from the mirror is:

• A. $(n-1)f$
• B. $\left(\frac{n-1}{n}\right)f$
• C. $\left(\frac{n+1}{n}\right)f$
• D. $\left(n+1\right)f$

Answer 1

The correct option is A $(n-1)f$

Magnification $m=-\frac{v}{u}=\frac{1}{n}$
$\Rightarrow v=\frac{-u}{n}$
Using mirror formula,
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\Rightarrow \frac{1}{f}=\frac{1}{\left(}+\frac{1}{u}\Rightarrow u=-\left(n-1\right)f$
The negative sign just symbolise that the image is on the left of the mirror.