The minimum distance between an object and its real image formed by a concave mirror is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → zero
A concave mirror forms a real image of an object placed beyond its focus. When the object is at the centre of curvature C, the image is formed at C itself, so the object and its image coincide.
With the Cartesian sign convention, put the object at C, so \( u=R \). Since \( R=2f \), \( u=2f \) (both negative for a concave mirror). The mirror equation gives:
\( \begin{aligned} \frac{1}{v} &= \frac{1}{f}-\frac{1}{u} \\ &= \frac{1}{f}-\frac{1}{2f} \\ &= \frac{1}{2f} \end{aligned} \)
\( v=2f \)
From the above, \( v=u \). Hence the real image lies on the object itself, and the distance between them is zero. A distance cannot be less than zero, so this is the minimum.