The formula to calculate the radius of curvature (R) and focal length (f) is:
\[ \frac{1}{O} + \frac{1}{I} = \frac{2}{R} = \frac{1}{f} \]
Where:
The mirror equation describes the relationship between the radius of curvature of a mirror and the focal length of the mirror.
Example 1:
Using the formula:
\[ \frac{1}{30} + \frac{1}{15} = \frac{1}{f} \]
\[ \frac{1}{f} = \frac{1}{30} + \frac{1}{15} = \frac{1}{30} + \frac{2}{30} = \frac{3}{30} = \frac{1}{10} \]
\[ f = 10 \text{ cm} \]
\[ R = 2 \times 10 = 20 \text{ cm} \]
Example 2:
Using the formula:
\[ \frac{1}{40} + \frac{1}{20} = \frac{1}{f} \]
\[ \frac{1}{f} = \frac{1}{40} + \frac{1}{20} = \frac{1}{40} + \frac{2}{40} = \frac{3}{40} \]
\[ f = \frac{40}{3} \approx 13.33 \text{ cm} \]
\[ R = 2 \times 13.33 \approx 26.67 \text{ cm} \]
