Question

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is \( -3 \), then the magnitude of the radius of curvature of the mirror is:

• A. 7.5 cm
• B. 30 cm
• C. 15 cm
• D. 3.75 cm

Hint:

For concave mirrors, use the mirror equation \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \), and the magnification to solve for unknown distances or focal lengths.

Answer 1

The Correct Option is C

The magnification \( m \) is given by: \[ m = -\frac{v}{u} \] Where \( v \) is the image distance and \( u \) is the object distance. Also, the mirror equation is: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Using the given magnification and the relation between focal length \( f \) and radius of curvature \( R \): \[ f = \frac{R}{2} \] By solving these equations, we find that the radius of curvature \( R = 15 \, {cm} \).