An object is placed at the centre of curvature C of a concave mirror of focal length 15 cm. State the position, size and nature of the image formed. Using the mirror formula, verify the image distance.
Generated by claude-sonnet-4-6 · 2026-06-26 01:12 · grounding rag
Model Answer
Position: At C (i.e., at 30 cm in front of the mirror)
Size: Same as the object
Nature: Real and inverted
Verification using mirror formula:
Given: f = −15 cm, u = −30 cm (object at C, so R = 2f = 30 cm)
$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
$$\frac{1}{v} = \frac{1}{-15} - \frac{1}{-30} = \frac{-2+1}{30} = \frac{-1}{30}$$
$$v = -30 \text{ cm}$$
Image is formed at C, 30 cm in front of the mirror. ✓
Source: Table 9.1 and Section 9.2.4, Chapter 9
Explanation
- From Table 9.1: when object is at C, image is also at C — same size, real, inverted.
- For mirror formula, use sign convention: distances in front of mirror are negative. f = −15 cm, u = −30 cm (since R = 2f).
- The calculated v = −30 cm confirms the image is at C, verifying the table result.
- Examiners award marks for: correct position/size/nature (1 mark) and correct mirror formula calculation (1 mark).