Question

The focal length $f$ is related to the radius of curvature $r$ of the spherical convex mirror by :

• A. $f = r$
• B. $f = -r$
• C. $f = -\frac{1}{2}r$
• D. $f = +\frac{1}{2}r$

Hint:

Convex mirrors have positive focal lengths, while concave mirrors have negative focal lengths.

Answer 1

The Correct Option is D

Step 1: For any spherical mirror, the magnitude of focal length $|f| = r/2$.
Step 2: By sign convention, for a convex mirror, both the focus and center of curvature lie behind the mirror (positive $x$-direction).
Step 3: Therefore, $f$ and $r$ are both positive. $f = +r/2$.