Question

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is:

• A. \( \frac{1}{2} \)
• B. 2
• C. 3
• D. \( \frac{1}{3} \)

Hint:

Remember, the magnification formula for mirrors relates the image size to the object distance and the focal length. For concave mirrors, the object distance is negative, while for convex mirrors it is positive.

Answer 1

The Correct Option is A

Employing the magnification formula for mirrors, \( m = \frac{f}{u-f} \), for a concave mirror with object distance \( u = -18 \, \text{cm} \) and focal length \( f = \frac{R}{2} = 6 \, \text{cm} \) (where \( R = 12 \, \text{cm} \)), the magnification is calculated as: \[ m_1 = \frac{6}{18 - 6} = \frac{1}{2} \]

For a convex mirror, with the same object distance and a positive focal length, the magnification is: \[ m_2 = \frac{6}{18 + 6} = \frac{1}{4} \] The ratio of the image sizes formed by the convex mirror to the concave mirror is therefore: \[ \frac{m_2}{m_1} = \frac{1/4}{1/2} = \frac{1}{2} \]

The final result is: \[ \frac{1}{2} \]