Question

A concave mirror gives an image three times as large as the object placed at a distance of 20 cm from it. For the image to be real, the focal length should be :

• A. $10\text{cm}$
• B. $15\text{cm}$
• C. $20\text{cm}$
• D. $30\text{cm}$

Answer 1

The correct option is B $15\text{cm}$


Magnification is –3 because image is real & inverted.
$m=\frac{-v}{u}$
$-3=\frac{-v}{u}$
$v=3u$.
given $u=-20\text{cm}$
$v=-60\text{cm}$
By using mirror formula
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{-60}+\frac{1}{(-20)}=\frac{1}{f}$
$f=-15\text{cm}$
Hence option (B) is correct.