Find the focal length of a convex mirror whose radius of curvature is 32 cm.
The focal length of the convex mirror is +16 cm.
Explanation
According to the textbook, for a spherical mirror of small aperture, the principal focus F lies mid-way between the pole P and the centre of curvature C. This relationship is expressed as f = R/2. The context from Example 9.1 demonstrates this formula for a convex mirror, showing that focal length equals half the radius of curvature. Since the principal focus of a convex mirror is behind the mirror, the focal length is taken as positive.
Solution Steps
Step 1: Given, Radius of curvature (R) = 32 cm
Step 2: For a spherical mirror, focal length (f) = R/2
Step 3: Substituting the value: f = 32/2 = 16 cm
Step 4: Since the principal focus of a convex mirror is behind the mirror, f = +16 cm