Mirror Equation Calculator

Calculate Radius of Curvature and Focal Length



Formula

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:

What is the Mirror Equation?

The mirror equation describes the relationship between the radius of curvature of a mirror and the focal length of the mirror.

Example Calculations

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:

\[ \frac{1}{40} + \frac{1}{20} = \frac{1}{f} \]

\[ \frac{1}{f} = \frac{1}{40} + \frac{1}{20} = \frac{1}{40} + \frac{2}{40} = \frac{3}{40} \]

\[ f = \frac{40}{3} \approx 13.33 \text{ cm} \]

\[ R = 2 \times 13.33 \approx 26.67 \text{ cm} \]