Question

An object is placed 50 cm from a lens which produces a virtual image at a distance of 10 cm in front of the lens. Calculate the focal length of the lens.

• A. -12.5 cm
• B. 12.5 cm
• C. -15 cm
• D. -50 cm

Answer 1

The correct option is A -12.5 cm

Distance between the object and the lens = -50 cm
Distance between the image and the lens = -10 cm
Focal length = ?
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{f}=\frac{1}{-10}-\frac{1}{-50}$
$=\frac{-1}{10}+\frac{1}{50}$
$=\frac{-5+1}{50}$
$=-\frac{4}{50}$
$-\frac{50}{4}$
The focal length of the lens is -12.5 cm and the negative sign indicates that the lens is concave.