Focal Length Of Concave Mirror

NCERT Class 12, Chapter 9 notes that for a concave mirror the focal length is half the radius of curvature, $f=\frac{R}{2}$. In this laboratory method, the object is moved until its real, inverted image forms at exactly the same position as the object; this coincidence happens only when the object sits at the centre of curvature, because rays from a point at C return to C. At that point the object distance equals the radius of curvature $R$, so the focal length is half of that measured distance, $f=\frac{R}{2}$. The option equating focal length to the object distance is wrong because that distance is the full radius, not the focal length. The option of twice the object distance is wrong because it doubles $R$ instead of halving it. The option claiming independence of object distance is wrong because the whole method relies on locating the specific distance where image and object coincide. This coincidence is detected experimentally by removing parallax between the object pin and its inverted image, adjusting until they move together when the eye is shifted sideways. The method is valued because it needs only a single distance measurement rather than separate object and image distances, reducing the sources of error. A consistency check confirms that the coincidence uniquely fixes the object at the centre of curvature at distance R, so halving that distance correctly yields the focal length R over two.