(a) A student has focussed the image of an object of height 3 cm on a white screen using a concave mirror of focal length 12 cm. If the distance of the object from the mirror is 18 cm, find the values of the following :
Generated by claude-sonnet-4-6 · 2026-06-15 06:49 · grounding rag
Model Answer
(i) Distance of the image from the mirror:
Given: h = +3 cm, f = −12 cm (concave), u = −18 cm
Using mirror formula:
$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
$$\frac{1}{v} = \frac{1}{-12} - \frac{1}{-18} = -\frac{1}{12} + \frac{1}{18} = \frac{-3+2}{36} = \frac{-1}{36}$$
$$v = -36 \text{ cm}$$
The image is formed 36 cm in front of the mirror (real and inverted).
(ii) Height of the image:
$$m = -\frac{v}{u} = -\frac{-36}{-18} = -2$$
$$h' = m \times h = -2 \times 3 = -6 \text{ cm}$$
The height of the image is 6 cm (negative sign indicates it is real and inverted).
Source: Chapter 9, Section 9.2.4 — Mirror Formula and Magnification
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Explanation
- Sign convention: For a concave mirror, f and u are both negative (distances measured in front of the mirror). Always assign signs before substituting.
- Examiners look for: correct substitution with signs, the mirror formula working shown step-by-step, and both answers stated clearly with units and nature.
- The negative value of h′ confirms the image is real and inverted — mentioning this adds quality to the answer.
- Object is between C and F (u = 18 cm, f = 12 cm), so the image is expected beyond C — v = 36 cm confirms this, consistent with Table 9.1.