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:
Show Hint
- \( \frac{1}{2} \)
- 2
- 3
- \( \frac{1}{3} \)
The Correct Option is A
Solution and Explanation
Using the magnification formula for mirrors: \[ m = \frac{f}{u-f} \] For the concave mirror, the object distance is \( u = -18 \, \text{cm} \), and the focal length is \( f = \frac{R}{2} = 6 \, \text{cm} \), where \( R = 12 \, \text{cm} \): \[ m_1 = \frac{6}{18 - 6} = \frac{1}{2} \]
For the convex mirror, the object distance is the same, and the focal length is positive: \[ m_2 = \frac{6}{18 + 6} = \frac{1}{4} \] Hence, the ratio of the sizes of the images formed by the convex mirror and the concave mirror is: \[ \frac{m_2}{m_1} = \frac{1/4}{1/2} = \frac{1}{2} \]
Thus, the correct answer is: \[ \frac{1}{2} \]
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