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

Concept:

Focal Length of a Spherical Mirror:

• The focal length (f) of a spherical mirror is related to its radius of curvature (r).
• A  convex mirror is a spherical mirror that curves outward.
• For any spherical mirror, the focal length is given by the formula:
• \(f = \frac{r}{2}\)
• Here,
  • f: Focal length, SI unit: meter (m), Dimensional Formula: [L]
  • r: Radius of curvature, SI unit: meter (m), Dimensional Formula: [L]
• For a convex mirror,  the focal length (f) is positive.
• Therefore, for a convex mirror, the focal length is:
• \(f = +\frac{r}{2}\)

Calculation:

Given,

Radius of curvature = r

We know that for a convex mirror,

\(f = +\frac{r}{2}\)

Therefore,

⇒ f = +1/2 r

Hence, the correct answer is option 3.