Question

The distance between an object and its doubly magnified image by a concave mirror is: [ Assume $f$ = focal length]

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

Answer 1

Answer: (A)

$3f/2$

The magnification is given as,

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

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

$v=-2u$

Ignoring the sign and using mirror formula, we get

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

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

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

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

Here, difference between object distance and image distance is also$u$.