Question

The distance between an object is doubly magnified by a concave mirror of focal length $f$ is

• A. $3f/2$
• B. $2f/3$
• C. $3f$
• D. Depend on whether the image is real or virtual

Answer 1

Answer: (D)

Depend on whether the image is real or virtual

Given,

Focal length, $f$

Magnification, $m$

Object distance, $u$

Image distance, $v$

Case I (Real image)

$m=-2$

$m=\frac{-v}{u}$

$-2=\frac{-v}{u}$

$v=2u$

Using mirror formula,

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

$\frac{1}{f}=\frac{1}{2u}+\frac{1}{u}$

$\frac{1}{f}=\frac{3}{2u}$

$u=\frac{3f}{2}$

Case II (Virtual image)

$m=2$

$2=\frac{-v}{u}$

$v=-2u$

Using mirror formula,

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

$\frac{1}{f}=\frac{1}{-2u}+\frac{1}{u}$

$\frac{1}{f}=\frac{-1+2}{2u}$

$u=\frac{f}{2}$

$\therefore$ Object distance depends on whether the image is real or virtual.