Reflection At Spherical Mirrors

A spherical mirror obeys the mirror equation $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$, while the linear magnification follows $m=-\frac{v}{u}$, both written in the Cartesian sign convention where distances measured against the incident light are negative. For a concave mirror the focal length is taken as negative, so $f=-20$ cm and the object distance is $u=-30$ cm. Rearranging gives $\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=-\frac{1}{20}+\frac{1}{30}=-\frac{1}{60}$, hence $v=-60$ cm. The magnification is $m=-\frac{v}{u}=-\frac{-60}{-30}=-2$, a real, inverted image twice the object size. Physically, rays diverging from the object converge after reflection from the concave surface, and the two standard construction rays—one travelling parallel to the principal axis then passing through the focus, and one heading toward the centre of curvature and retracing its path—intersect to fix the real image. The negative sign of $m$ encodes the inversion, while its magnitude exceeding unity signals genuine enlargement of the object. The value $+2$ is wrong because it ignores the inversion implied by the negative sign. The value $-0.5$ is wrong as it inverts the ratio $v/u$. The value $-3$ is wrong since it would require an image distance of 90 cm. This is the standard NCERT treatment of image formation by concave mirrors. A plausibility check confirms that an object lying between the focus and the centre of curvature must yield a magnified inverted image, consistent with $|m|>1$.