Mirror Equation Calculator
Calculate image distance, object distance, or focal length for mirrors
Use positive values. Sign convention: negative for virtual objects.
Positive for concave mirrors, negative for convex mirrors
How to Use This Calculator
Select What to Calculate
Choose whether you want to calculate the image distance, focal length, or object distance.
Enter Known Values
Input the two known values. For object and image distances, use positive values for real objects/images. For focal length, use positive for concave mirrors (converging) and negative for convex mirrors (diverging).
Calculate
Click the "Calculate" button to get the unknown value. The result shows the distance in meters and centimeters, and indicates if it's a virtual image/object or convex mirror.
Formula
1/f = 1/u + 1/v
Where:
- f = Focal length (in meters)
- u = Object distance (in meters)
- v = Image distance (in meters)
Sign Convention:
- f: Positive for concave mirrors, negative for convex mirrors
- u: Usually positive (object in front of mirror)
- v: Positive for real images (in front), negative for virtual images (behind)
Example Calculation:
For a concave mirror with f = 0.1 m and object at u = 0.2 m:
1/v = 1/0.1 - 1/0.2 = 10 - 5 = 5
v = 1/5 = 0.2 m
The image is at 20 cm, same distance as object (magnification = -1).
About Mirror Equation Calculator
The mirror equation relates the object distance, image distance, and focal length of a mirror. It's identical in form to the thin lens equation and is fundamental to understanding how mirrors form images. This calculator helps you solve for any of the three variables when you know the other two, making it useful for designing optical systems, understanding image formation, and solving physics problems.
When to Use This Calculator
- Optics Problems: Solve physics and optics homework problems involving mirrors
- Optical Design: Design systems using mirrors and calculate image positions
- Telescope Design: Calculate focal lengths and image positions for reflecting telescopes
- Education: Understand mirror image formation and the mirror equation
- Research: Analyze optical systems and mirror configurations
Why Use Our Calculator?
- ✅ Three Calculations: Calculate image distance, focal length, or object distance
- ✅ Instant Results: Get accurate calculations immediately
- ✅ Multiple Units: Results in meters and centimeters
- ✅ Sign Convention: Handles positive and negative values correctly
- ✅ Educational: Includes formula explanations and examples
- ✅ 100% Free: No registration required
Common Applications
Telescopes: Reflecting telescopes use mirrors to focus light. The mirror equation helps calculate focal lengths and image positions, essential for telescope design and alignment.
Optical Instruments: Many optical instruments use mirrors for imaging, folding optical paths, or creating specific optical configurations. Understanding the mirror equation is essential for their design.
Physics Education: The mirror equation is a fundamental concept in optics education, helping students understand how mirrors form images and the relationship between object and image positions.
Tips for Best Results
- Use consistent units (meters for all distances)
- For concave mirrors, focal length is positive (converging)
- For convex mirrors, focal length is negative (diverging)
- Real images have positive image distances (in front of mirror)
- Virtual images have negative image distances (behind mirror)
- When object is at focal point, image is at infinity
- When object is at infinity, image is at focal point
Frequently Asked Questions
What's the difference between concave and convex mirrors?
Concave mirrors (converging) have a positive focal length and can form real or virtual images depending on object position. Convex mirrors (diverging) have a negative focal length and always form virtual, upright, and reduced images.
What is a real image vs a virtual image?
A real image is formed where light rays actually converge and can be projected on a screen. It has a positive image distance. A virtual image is formed where light rays appear to converge but don't actually meet; it cannot be projected and has a negative image distance.
Why is the mirror equation the same as the lens equation?
Both mirrors and lenses follow the same mathematical relationship because they both focus light. The sign conventions differ slightly, but the fundamental equation 1/f = 1/u + 1/v applies to both. This is a result of the similar geometric optics principles governing both.
What happens when the object is at the focal point?
When u = f, the image distance becomes infinite (parallel rays). This means the image is formed at infinity, and the rays are parallel after reflection. This is useful for creating collimated light beams.
Can I use this for spherical mirrors?
Yes, the mirror equation works for spherical mirrors (both concave and convex) in the paraxial approximation (small angles near the optical axis). For large angles or non-spherical mirrors, more complex calculations are needed.