An object is placed at the FOCUS of a concave mirror ($u = f$, both negative). The image forms at
Athe focus itself
Bthe centre of curvature (at $2f$)
Cinfinity
Dthe pole of the mirror
Answer & Solution
Correct answer: C. infinity
1. Mirror formula: $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$.
2. Substitute $u = f$ (both negative): $\dfrac{1}{v} + \dfrac{1}{f} = \dfrac{1}{f}$.
3. Rearrange: $\dfrac{1}{v} = 0$, so $v \to \infty$.
4. The image forms at INFINITY — meaning the rays emerge PARALLEL after reflection.
5. This is the principle of REVERSIBILITY: an object at the focus of a concave mirror produces a parallel beam (just like a parallel beam from infinity focuses at the focal point — the path of light is reversible).
6. Used in headlights, torches, satellite dishes — source at the focus, parallel output beam.
7. Options A, B, D would require different $u$ values.
_Source: syllabus Physics Part 2, Ch 9, §9.2.5 (Mirror formula — object at focus case), p. 4–5._
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