A student sets up an experiment with a concave mirror. She measures the object distance as 20 cm and the image distance as 30 cm, and writes both values as positive in the mirror formula. Her teacher marks this as incorrect. Explain what the student did wrong and write the correct signs for both distances, justifying your answer using the New Cartesian Sign Convention.
Generated by claude-sonnet-4-6 · 2026-06-26 01:13 · grounding rag
Model Answer
Error made by the student: She wrote both object distance (u) and image distance (v) as positive, which violates the New Cartesian Sign Convention.
Correct signs and justification:
- Object distance (u) = −20 cm (negative): The object is always placed to the left of the mirror. Since distances measured to the left of the pole are negative, u must be −20 cm.
- Image distance (v) = −30 cm (negative): For a concave mirror, a real image is formed in front of the mirror, i.e., to the left of the pole. Distances measured to the left are negative, so v = −30 cm.
Both distances should be negative. Writing them as positive gives an incorrect result when applying the mirror formula $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$.
Source: Chapter 9, Section 9.2.3 & 9.2.4
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Explanation
What examiners look for:
- Clearly stating what the student did wrong (both values positive — 1 mark).
- Correct sign for u with reason (1 mark).
- Correct sign for v with reason — a real image forms in front of the mirror, hence negative (1 mark).
Key rule to remember: In New Cartesian Sign Convention, the object is always to the left → u is always negative for mirrors. A real image also forms in front (left side) of a concave mirror → v is negative. Only a virtual image (behind the mirror, right side) gives positive v.