A 4 cm tall object is placed 30 cm in front of a concave mirror of focal length 10 cm. Using the mirror formula and magnification formula, find: (i) the image distance, (ii) the height of the image, and (iii) whether the same object placed 30 cm in front of a convex lens of focal length 10 cm would give an image on the same side or the opposite side of the device compared to the object. Justify your answer for part (iii) without calculation.
Generated by claude-sonnet-4-6 · 2026-06-26 01:16 · grounding rag
Model Answer
(i) Image distance (Concave Mirror):
Given: h = +4 cm, u = –30 cm, f = –10 cm
Using mirror formula: $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
$$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-10} - \frac{1}{-30} = -\frac{1}{10} + \frac{1}{30} = \frac{-3+1}{30} = \frac{-2}{30}$$
$$v = -15 \text{ cm}$$
The image is formed 15 cm in front of the mirror (real and inverted).
(ii) Height of image:
$$m = -\frac{v}{u} = -\frac{(-15)}{(-30)} = -\frac{1}{2}$$
$$h' = m \times h = -\frac{1}{2} \times 4 = -2 \text{ cm}$$
The image is 2 cm tall, real and inverted.
(iii) Convex lens (f = +10 cm, u = –30 cm):
The object is placed beyond 2F of the convex lens (since 2f = 20 cm < 30 cm). A convex lens forms a real, inverted image on the opposite side of the lens from the object. For a concave mirror, the real image forms on the same side as the object. Thus, the two devices give real images on opposite sides relative to the object's position.
Source: Chapter 9, Sections 9.2.4 and 9.3.7
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Explanation
- Always apply New Cartesian Sign Convention: distances measured in the direction of incident light are positive; against it are negative. For a concave mirror, both u and f are negative.
- The mirror formula is $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$; the lens formula is $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ — note the difference in signs between the two formulas.
- For part (iii), no calculation is needed — the justification is conceptual: a convex lens always forms a real image on the opposite side to the object (when object is beyond F), whereas a concave mirror forms a real image on the same side as the object. Examiners expect this distinction clearly stated.
- Negative h′ confirms the image is inverted and real — mention this explicitly for full marks.