Q1. [1] § 9.2.1 Image Formation by Spherical Mirrors § 9.2.4 Mirror Formula and Magnification
An object is placed at a distance of 30 cm from the pole of a concave mirror. If its real and inverted image is formed at 60 cm in front of the mirror, the focal length of the mirror is :
- (A) – 15 cm
- (B) – 20 cm
- (C) + 20 cm
- (D) + 15 cm
Previously asked in CBSE board exam
2025 31/2/1 Q12
Generated by claude-sonnet-4-6 · 2026-06-15 06:48 · grounding rag
Model Answer
(B) – 20 cm
Using mirror formula: $u = -30$ cm, $v = -60$ cm (real image, in front of mirror).
$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{-60} + \frac{1}{-30} = \frac{-1-2}{60} = \frac{-3}{60} = \frac{1}{-20}$$
So, $f = -20$ cm.
Explanation
Apply the mirror formula with correct signs (New Cartesian Sign Convention): object and real image both in front of the mirror, so both u and v are negative. A concave mirror always has a negative focal length. Students commonly make sign errors — always assign signs before substituting.
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