Mirror Equation Calculator

Historical Background

Mirrors have been used since antiquity to observe and manipulate light. The understanding of mirror equations provides critical insights into optics. Historically, spherical mirrors helped in comprehending focal lengths, which later facilitated the development of lenses and advanced optical instruments.

Formula

The mirror equation is fundamental in geometric optics and can be expressed as:

\[ \frac{1}{O} + \frac{1}{I} = \frac{2}{R} = \frac{1}{f} \]

where:

• \( O \) is the object distance from the mirror,
• \( I \) is the image distance from the mirror,
• \( R \) is the radius of curvature,
• \( f \) is the focal length.

Example Calculation

Let's calculate the focal length and radius of curvature if the object distance is 30 cm and the image distance is 10 cm:

\[ \frac{1}{O} + \frac{1}{I} = \frac{1}{30} + \frac{1}{10} = 0.0333 + 0.1 = 0.1333 \]

Thus, the focal length is:

\[ f = \frac{1}{0.1333} \approx 7.5 \, \text{cm} \]

The radius of curvature is twice the focal length:

\[ R = 2 \cdot 7.5 \approx 15 \, \text{cm} \]

Common FAQs

1. What is the mirror equation used for?

   • It is used to find the focal length and radius of curvature of a curved mirror based on known distances of the object and its reflected image.

2. What is focal length?

   • The focal length is the distance at which a mirror or lens focuses light to a single point.

3. How does the radius of curvature relate to the focal length?

   • The radius of curvature is twice the focal length, or \( R = 2f \).

Understanding the mirror equation is essential for designing optical systems, telescopes, and cameras, making it a fundamental tool in optics and physics.