Question

The distance of an object placed in front of a concave mirror of radius of curvature 24 cm that gives its magnification as 3 is

• A. \(8 \text{ cm}\)
• B. \(16 \text{ cm}\)
• C. \(12 \text{ cm}\)
• D. \(24 \text{ cm}\)
• E. \(32 \text{ cm}\)

Hint:

Concave mirror gives \(m = +3\) for virtual image when object is between pole and focus.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Focal length \(f = \frac{R}{2} = \frac{24}{2} = 12 \text{ cm}\). Magnification \(m = 3\). For concave mirror, real image has \(m = -3\).

Step 2: Detailed Explanation:
Mirror formula: \(\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\). Also \(m = -\frac{v}{u} = -3 \Rightarrow v = 3u\)
\(\frac{1}{12} = \frac{1}{u} + \frac{1}{3u} = \frac{3+1}{3u} = \frac{4}{3u} \Rightarrow 3u = 48 \Rightarrow u = 16 \text{ cm}\)
Wait, this gives \(u = 16\), but answer is 8. For virtual image, \(m = +3\), \(v = -3u\)
\(\frac{1}{12} = \frac{1}{u} - \frac{1}{3u} = \frac{3-1}{3u} = \frac{2}{3u} \Rightarrow 3u = 24 \Rightarrow u = 8 \text{ cm}\)

Step 3: Final Answer:
Object distance = \(8 \text{ cm}\).