1. What is Mirror Radius?

The mirror radius (R) is the distance from the center of curvature to the mirror's surface. It's directly related to the focal length (f) of the mirror through the simple relationship R = 2f.

2. How Does the Calculator Work?

The calculator uses the fundamental mirror formula:

Where:

• \( R \) — Radius of curvature (meters)
• \( f \) — Focal length (meters)

Explanation: For spherical mirrors, the center of curvature is located at twice the focal length from the mirror's surface. This relationship holds true for both concave and convex mirrors.

3. Importance of Mirror Radius Calculation

Details: Knowing the mirror radius is essential for understanding the mirror's optical properties, designing optical systems, and predicting image formation characteristics.

4. Using the Calculator

Tips: Simply enter the focal length of the mirror in meters. The calculator will compute the radius of curvature. The focal length must be a positive value.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for both concave and convex mirrors?
A: Yes, the relationship R = 2f applies to both concave and convex spherical mirrors.

Q2: What's the difference between focal length and radius of curvature?
A: The focal length is the distance from the mirror to the focal point, while the radius is the distance to the center of curvature (which is twice the focal length).

Q3: Can this be used for parabolic mirrors?
A: The formula is exact for spherical mirrors and approximately correct for parabolic mirrors when the aperture is small compared to the radius.

Q4: How does mirror radius affect image formation?
A: Larger radius mirrors (with longer focal lengths) produce less curved images and have weaker magnification compared to smaller radius mirrors.

Q5: What units should I use?
A: The calculator uses meters, but you can use any unit as long as you're consistent (the result will be in the same units as your input).