A concave mirror has a focal length of –10 cm. Using the mirror formula, find the object distance if the image is formed at –30 cm. What does the negative sign of the image distance tell you about the nature of the image? Justify your answer using the New Cartesian Sign Convention.
Generated by claude-sonnet-4-6 · 2026-06-26 01:13 · grounding rag
Model Answer
Given: f = –10 cm, v = –30 cm, u = ?
Using the mirror formula:
$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
$$\frac{1}{u} = \frac{1}{f} - \frac{1}{v} = \frac{1}{-10} - \frac{1}{-30} = -\frac{1}{10} + \frac{1}{30} = \frac{-3+1}{30} = \frac{-2}{30}$$
$$u = -15 \text{ cm}$$
The object is placed 15 cm in front of the mirror.
Nature of image: The negative sign of image distance (v = –30 cm) indicates the image is formed in front of the mirror (on the same side as the object). According to New Cartesian Sign Convention, distances measured to the left of the pole are negative. Hence, the image is real and inverted.
Source: Chapter 9, Section 9.2.3 and 9.2.4
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Explanation
- Examiners expect the full substitution step shown clearly — don't skip arithmetic.
- Two things are rewarded: (1) correct numerical value of u with sign, and (2) correct interpretation of negative v using sign convention terminology ("in front of mirror → real and inverted").
- Always state the sign convention rule explicitly: distances to the left of pole are negative → image in front = real.
- A common mistake is forgetting to use negative signs for f and v when substituting — always apply New Cartesian Sign Convention before calculating.