Question

At what distance from a concave mirror of focal length 10 cm must an object be placed in order that an image double its size may be obtained?

• A. 5 cm only
• B. 15 cm only
• C. either 5 cm or 15 cm
• D. at 10 cm

Answer 1

The correct option is C either 5 cm or 15 cm

$m=\frac{I}{O}=\frac{-v}{u}=\pm 2$

Case-1

$u=2v$

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

$\frac{1}{u}+\frac{1}{2u}=\frac{-1}{10}$

$\therefore u=-15$cm

case-2

$u=-2v$

$\frac{1}{u}-\frac{1}{2u}=\frac{-1}{10}\Rightarrow \frac{2-1}{2u}=\frac{-1}{10}$

$\therefore u=-5cm$

$\therefore u=-5$ or $-15$.