Question

The image formed by a convex mirror of focal length 30 cm is a quarter of the size of the object. The distance of the object from the mirror is

• A. 30 cm
• B. 90 cm
• C. 120 cm
• D. 60 cm

Hint:

For convex mirrors, the image formed is always virtual, erect, and smaller than the object.

Answer 1

The Correct Option is B

For a convex mirror, the magnification \( m \) is given by: \[ m = \frac{\text{image size}}{\text{object size}} = \frac{1}{4} \] The magnification formula for a mirror is: \[ m = \frac{v}{u} \] Where: - \( v \) is the image distance, - \( u \) is the object distance. From the mirror equation: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Where \( f = 30 \, \text{cm} \) is the focal length. Using the magnification relation \( m = \frac{1}{4} \), the object distance \( u \) can be determined to be \( 90 \, \text{cm} \). Thus, the distance of the object from the mirror is \( \boxed{90 \, \text{cm}} \).