An object is placed at a distance of 60 cm from a concave lens of focal length 30 cm. Use lens formula to find the position of the image formed in this case.
Generated by claude-sonnet-4-6 · 2026-06-15 06:48 · grounding rag
Model Answer
Given: u = –60 cm, f = –30 cm (concave lens)
Using lens formula:
$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
$$\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{-30} + \frac{1}{-60}$$
$$\frac{1}{v} = \frac{-2-1}{60} = \frac{-3}{60} = \frac{-1}{20}$$
$$v = -20 \text{ cm}$$
The image is formed 20 cm in front of the lens (on the same side as the object). It is virtual and erect.
Source: Light – Reflection and Refraction, Chapter 9
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Explanation
- Always assign signs first: object distance u is negative (object on left), focal length f is negative for concave lens.
- Use $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ carefully — rearrange to find v.
- A negative v confirms the image is on the same side as the object → virtual and erect, which is consistent with a concave lens always forming such images.
- Examiners award 1 mark for correct substitution/working and 1 mark for the correct answer with sign and position statement.