alleryThe relationship between the focal length $f$ and the radius of curvature $R$ for a SPHERICAL MIRROR is
A$f = 2R$
B$f = R$
C$f = R/2$
D$f = R^2/2$
Answer & Solution
Correct answer: C. $f = R/2$
1. syllabus derives the focal-length / radius relation for a spherical mirror, for rays close to the principal axis (paraxial approximation).
2. The focal point lies at HALF the distance from the pole to the centre of curvature.
3. So $f = R/2$. The same relation holds for concave and convex mirrors (sign-aware).
4. Numerical example: a concave mirror with $R = 20\,\text{cm}$ has $f = 10\,\text{cm}$.
5. Options A and B are too large by factors of 4× and 2×. Option D has wrong dimensions.
_Source: syllabus Physics Part 2, Ch 9, §9.2.4 (Focal length of spherical mirrors, Eq. 9.3), p. 4._
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