Home › UP Board Class 12 › physics › Ray Optics and Optical Instruments › An object is placed at the FOCUS of a concave mi…
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: NCERT Class 12 Physics Part 2, Ch 9, §9.2.5 (Mirror formula — object at focus case), p. 4–5._
Related questions
The phenomenon by which the apparent position of a star near the horizon appears slightly When light travels from one medium to another, which property of the wave REMAINS UNCHANGELight passing through a PRISM is dispersed because different colours of light haveA converging lens of focal length $20\,\text{cm}$ produces a real image at $30\,\text{cm}$Optical fibres use TOTAL INTERNAL REFLECTION to transmit light over long distances. The MATwo thin lenses of powers $+5\,\text{D}$ and $-3\,\text{D}$ are placed in CONTACT. The totThe POWER of a lens (in diopters, D) is defined asThe LENSMAKER'S formula for a thin lens of refractive index $n$ (in air) with radii of cur