Question

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is:

• A. 45 cm
• B. 7.5 cm
• C. 22.5 cm
• D. 15 cm

Hint:

The image formed by a convex mirror is virtual and behind the mirror. The distance between two mirrors can be determined by the image formed by the first mirror.

Answer 1

The Correct Option is B

For the convex mirror, the mirror formula is: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Given: - \( f = 30 \, \text{cm} \), - \( u = -30 \, \text{cm} \). Substitute the values: \[ \frac{1}{30} = \frac{1}{v} + \frac{1}{-30} \] \[ \frac{1}{v} = \frac{1}{30} + \frac{1}{30} = \frac{2}{30} \] \[ v = 15 \, \text{cm} \] The distance between the two mirrors is equal to the image distance produced by the convex mirror, which is 15 cm.
Thus, the correct answer is (2).