Question

The radius of curvature of a spherical mirror is \(20\text{ cm}\). What is its focal length?

Hint:

The focal length is exactly half of the radius of curvature.

Answer 1

Step 1: Understanding the Concept:
For spherical mirrors with small apertures, there is a direct mathematical relationship between the radius of curvature and the focal length.

Step 2: Key Formula or Approach:
Focal length (\(f\)) = \(\frac{\text{Radius of curvature }(R)}{2}\)

Step 2: Detailed Explanation:
Given:
Radius of curvature, \(R = 20\text{ cm}\).
Using the formula:
\[ f = \frac{R}{2} \] \[ f = \frac{20}{2} \] \[ f = 10\text{ cm} \]
Step 3: Final Answer:
The focal length of the mirror is \(10\text{ cm}\).