The radius of curvature of a spherical mirror is 20 cm. What is its focal length?
Given: Radius of curvature (R) = 20 cm.
Formula: The focal length of a spherical mirror is equal to half its radius of curvature. f = R / 2
Calculation: f = 20 cm / 2 f = 10 cm
The focal length of the spherical mirror is 10 cm.
Explanation
The textbook context explicitly states that 'The focal length of a spherical mirror is equal to half its radius of curvature' and defines the relationship R = 2f. By rearranging this formula to f = R/2 and substituting the given value of 20 cm, we calculate the focal length. This relationship holds true for spherical mirrors of small apertures.
Solution Steps
Step 1: Identify the given value: Radius of curvature (R) = 20 cm.
Step 2: State the relationship: The focal length (f) is half the radius of curvature (R). Formula: f = R/2.
Step 3: Perform the calculation: f = 20 cm / 2 = 10 cm.