A physics teacher demonstrates an experiment with a concave mirror of focal length 15 cm. She places a lighted candle at four different positions: (a) 40 cm, (b) 30 cm, (c) 15 cm, and (d) 10 cm from the mirror. She asks students to predict the nature, position and size of the image in each case.
(i) For object distance 40 cm, what is the image distance? Is the image real or virtual? [1 mark]
(ii) At which of the four positions will the image be the same size as the object? [1 mark]
(iii) At which position will no image be formed on the screen? Why? [1 mark]
(iv) For object distance 10 cm, state the nature and approximate position of the image. [1 mark]
Generated by claude-sonnet-4-6 · 2026-06-26 01:13 · grounding rag
Model Answer
(i) Using mirror formula: f = −15 cm, u = −40 cm
$$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-15} - \frac{1}{-40} = \frac{-8+3}{120} = \frac{-5}{120}$$
∴ v = −24 cm. The image is formed 24 cm in front of the mirror. It is real and inverted.
(ii) The image is the same size as the object when the object is placed at C (centre of curvature), i.e., at 30 cm (= 2f) from the mirror.
(iii) When the candle is placed at F (15 cm), no image is formed on the screen. This is because the reflected rays become parallel to the principal axis and meet only at infinity.
(iv) Object at 10 cm is between P and F. The image is formed behind the mirror, is virtual, erect and enlarged.
Source: Chapter 9, Section 9.2.1 (Table 9.1) and Section 9.2.4
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Explanation
- (i) Apply the mirror formula with sign convention (concave mirror: f negative, object distance negative). v = −24 cm confirms real image (negative v in concave mirror context).
- (ii) Table 9.1 directly states: object at C → image at C, same size. C = 2f = 30 cm.
- (iii) Object at F → reflected rays are parallel → image at infinity → no image on screen. Examiners expect the reason about parallel rays.
- (iv) Object between P and F → virtual, erect, enlarged image behind mirror. This is the standard result from Table 9.1. No calculation needed for 1 mark.