What is the relationship between the focal length (f) and the radius of curvature (R) of a spherical mirror? Using this relationship, find the focal length of a concave mirror whose radius of curvature is 24 cm.
Generated by claude-sonnet-4-6 · 2026-06-26 01:10 · grounding rag
Model Answer
The radius of curvature (R) of a spherical mirror is twice its focal length (f):
$$R = 2f \quad \text{or} \quad f = \frac{R}{2}$$
Given: R = 24 cm (concave mirror)
$$f = \frac{R}{2} = \frac{24}{2} = -12 \text{ cm}$$
The focal length of the concave mirror is 12 cm (negative sign indicates concave mirror).
Source: Chapter 9, Section 9.2 – Spherical Mirrors
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Explanation
- The key formula $R = 2f$ must be stated first — that fetches 1 mark.
- The calculation with correct answer fetches the second mark.
- For a concave mirror, focal length is negative by the New Cartesian Sign Convention; mention it briefly to show awareness.
- Don't confuse R/2 with 2R — a common slip.