AI-generated practice question — model-generated for extra practice, not a previous-year CBSE board question.
The student's claim is correct — both formulae give a negative value of m for a real, inverted image. Here's why:
For a spherical mirror: Object distance u is negative (object on left). A real image forms in front of the mirror, so v is also negative. Using $m = -v/u$:
$$m = -\frac{(-v)}{(-u)} = -\frac{v}{u} \Rightarrow \text{negative}$$
For a lens: u is negative (object on left), v is positive (real image on opposite side). Using $m = v/u$:
$$m = \frac{(+v)}{(-u)} \Rightarrow \text{negative}$$
Both give m < 0 for a real, inverted image. The difference in formula form (−v/u vs v/u) compensates for the fact that in a mirror, both u and v are negative, while in a lens, u is negative but v is positive.
Source: Chapter 9, Sections 9.2.4 and 9.3.7
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Examiners look for: (1) correct sign assignment using New Cartesian Convention, (2) numerical substitution showing sign of m for each case, (3) a clear concluding statement that both are consistent. The key insight is that the "extra negative" in the mirror formula exists precisely because real images in mirrors have negative v (unlike lenses), so the two formulas are deliberately written to yield the same physical result.