An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position of the image formed by the mirror.
Generated by claude-sonnet-4-6 · 2026-06-15 06:51 · grounding rag
Model Answer
Given: u = −10 cm, f = +15 cm (convex mirror)
Using mirror formula:
$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
$$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{+15} - \frac{1}{-10} = \frac{1}{15} + \frac{1}{10} = \frac{2+3}{30} = \frac{5}{30}$$
$$v = +6 \text{ cm}$$
The image is formed 6 cm behind the mirror. It is virtual and erect.
Source: Chapter 9, Section 9.2.4 (Mirror Formula)
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Explanation
- For a convex mirror, both f and v are always positive (behind the mirror), and u is negative.
- The positive value of v confirms the image is virtual and behind the mirror — consistent with Table 9.2.
- Examiners award 1 mark for correct substitution/formula and 1 mark for the correct answer with nature of image. Always state the nature explicitly.