Mirror Equation Calculator
Calculate image distance and magnification for curved mirrors using 1/f = 1/dₒ + 1/dᵢ. Analyze concave and convex mirrors used in telescopes, vehicle mirrors, and solar concentrators.
This free online mirror equation calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Mirror Equation Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Mirror Equation Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Mirror Equation Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Mirror Equation Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
About This Calculator
The Mirror Equation Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate image distance and magnification for curved mirrors using 1/f = 1/dₒ + 1/dᵢ. Analyze concave and convex mirrors used in telescopes, vehicle mirrors, and solar concentrators. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.
About Mirror Equation Calculator
The Mirror Equation Calculator determines image position and magnification for spherical mirrors. Concave mirrors (positive f) can form real or virtual images depending on object position, while convex mirrors (negative f) always produce virtual, upright, reduced images. This equation has the same form as the thin lens equation but applies to reflecting surfaces. Curved mirrors are used in telescopes (Hubble uses a 2.4 m concave mirror), car side mirrors ('objects may be closer than they appear'), makeup mirrors, solar furnaces, and satellite dishes.
The Math Behind It
Formula Reference
Mirror Equation
1/f = 1/dₒ + 1/dᵢ
Variables: f = focal length (R/2), dₒ = object distance, dᵢ = image distance
Magnification
M = −dᵢ/dₒ
Variables: M < 0: inverted, M > 0: upright
Worked Examples
Example 1: Concave Mirror
f = 15 cm, object at 30 cm
Image at 30 cm, same size, inverted (object at center of curvature).
Example 2: Convex Mirror
f = −20 cm, object at 40 cm
Virtual image 13.33 cm behind mirror, reduced to 1/3 size, upright.
Common Mistakes & Tips
- !Mixing up sign conventions between mirrors and lenses — in mirrors, real images form on the same side as the object.
- !Forgetting that f = R/2 for spherical mirrors.
- !Ignoring spherical aberration in large-aperture mirrors.
Related Concepts
Used in These Calculators
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Frequently Asked Questions
Why do car side mirrors say 'objects may be closer'?
Convex mirrors produce reduced virtual images (|M| < 1). Objects appear smaller and thus farther away than they are. The warning reminds drivers that the actual distance is less than perceived.
How does a telescope mirror work?
A large concave parabolic mirror collects parallel light from distant stars and focuses it at the focal point. Larger mirrors collect more light, enabling observation of fainter objects. The Hubble Space Telescope uses a 2.4 m primary mirror.
Can a mirror equation predict image quality?
The basic equation predicts position and size but not quality. Aberrations (spherical, coma, astigmatism) require more sophisticated analysis. Parabolic mirrors eliminate spherical aberration for on-axis objects.