Question

The relationship between the radius of curvature R and focal length f of a spherical mirror of small aperture could be represented as:

• A. R = 1/f
• B. R = 2f
• C. R = 3f
• D. R = f

Hint:

The focus of a spherical mirror is always halfway to its center of curvature:
\(f = \frac{R}{2}\) or \(R = 2f\).
Keep this simple relation in mind for numerical problems.

Answer 1

The Correct Option is B

Step 1: Set up the geometry.
Let \(P\) be the pole of the mirror and \(C\) its centre of curvature, so the distance \(PC\) is by definition the radius of curvature \(R\).
Step 2: Locate the focus within that geometry.
For a mirror of small aperture, the principal focus \(F\) lies exactly midway between \(P\) and \(C\), so the focal length \(f = PF\) is half of \(PC\).
Step 3: Write this as an equation and solve for R.
From \(f = R/2\), multiplying both sides by 2 gives \[ R = 2f \] which holds for concave and convex mirrors alike under the small aperture approximation.
\[ \boxed{R = 2f} \]