Question

A spherical mirror produces an image of magnification –1 on a screen placed at a distance of 50 cm from the mirror. What is the focal length of the mirror?

• A. + 32 cm
• B. - 32 cm
• C. - 25 cm
• D. + 25 cm

Answer 1

The correct option is C - 25 cm

As the magnification is negative, the image formed is real and inverted and located in front of the mirror.
Therefore, v = –50 cm
Since,
Magnification, $m=\frac{-v}{u}=-1$
u = –50 cm
By using the mirror formula, we get,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{f}=\frac{1}{-50}+\frac{1}{-50}=\frac{-1}{25}$
f = –25 cm