Question

A concave mirror of focal length $f$ produces an image $P$ time the size of the object. If the image is real, then the distance of the object from the mirror is

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

Answer 1

Answer: (D)

Given, Magnification, $M=\frac{I}{O}=-\frac{v}{u}=-P$
Or $v=uP.$
Using mirror's formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
Here, the image of the real object is also real, therefore, v.u.f, all are on the negative side.
Hence, $\frac{1}{-uP}+\frac{1}{-u}=\frac{1}{-f}$
$\Rightarrow \frac{1}{u}\left(\frac{1}{P}+1\right)=\frac{1}{f}$
$\Rightarrow u=\left(\frac{P+1}{P}\right)f$