Mirror Equation
The mirror equation 1/f = 1/d_o + 1/d_i relates focal length to object and image distances for spherical mirrors.
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Concave mirrors: real images when object beyond F. Convex mirrors: always virtual, upright, reduced images. Focal length f = R/2 for spherical mirrors. Magnification M = -d_i/d_o; negative M means inverted.
Ready to run the numbers?
Why: Essential for telescopes, reflectors, and understanding image formation.
How: Sign conventions: d_o > 0 (real object), d_i > 0 (real image), f > 0 (concave), f < 0 (convex).
Run the calculator when you are ready.
Mirror Parameters
Image Distance
300.00 mm
In front of mirror (real)
Magnification
-2.00ร
Inverted
Image Height
40.00 mm
Magnified
Image Type
Real
Inverted
Focal Length
100.00 mm
Radius
200.00 mm
F-Number
f/2.00
Optical Power
10.00 D
Diffraction Limit
2.76"
Light Gathering
51.02ร
Step-by-Step Calculation
Visualizations
For educational and informational purposes only. Verify with a qualified professional.
๐ฌ Physics Facts
Concave mirrors form real, inverted images when object is beyond focal point.
โ HyperPhysics
Convex mirrors always produce virtual, upright, reduced images.
โ Physics Classroom
Focal length f = R/2 for spherical mirrors of radius R.
โ MIT OCW
Negative magnification indicates inverted image.
โ Optics Textbooks
The mirror equation relates the focal length of a curved mirror to the distances of the object and image from the mirror. It applies to both concave (converging) and convex (diverging) mirrors.
The Equation
Also: f = R/2
Sign Convention
- โข Concave mirror: f > 0
- โข Convex mirror: f < 0
- โข Real image: di > 0
- โข Virtual image: di < 0
Reference: Image Formation Cases
| Object Position | Image Position | Image Type | Size |
|---|---|---|---|
| At infinity | At F | Real | Point |
| Beyond C | Between F and C | Real | Diminished |
| At C | At C | Real | Same size |
| Between F and C | Beyond C | Real | Magnified |
| At F | At infinity | - | - |
| Between F and mirror | Behind mirror | Virtual | Magnified |
๐ Key Takeaways
- โข The mirror equation 1/f = 1/do + 1/di relates focal length to object and image distances
- โข Concave mirrors can form both real and virtual images depending on object position
- โข Convex mirrors always form virtual, diminished, upright images
- โข Magnification m = -di/do determines image size and orientation
- โข Focal length f = R/2 where R is the radius of curvature
๐ก Did You Know
The largest optical telescope mirrors use concave parabolic surfaces to eliminate spherical aberration. The Hubble Space Telescope's primary mirror is 2.4 meters in diameter with a focal length of 57.6 meters, creating an f/24 system perfect for deep space observations.
Car side mirrors use convex surfaces to provide a wider field of view, trading image size for safety. The "Objects in mirror are closer than they appear" warning compensates for the reduced magnification.
๐ฏ Expert Tips
- โข For telescope mirrors, use parabolic surfaces (not spherical) to eliminate coma and spherical aberration
- โข When object is at focal point, image forms at infinity - useful for collimating light sources
- โข Negative magnification indicates inverted image; positive means upright
- โข For photography, concave mirrors can create interesting bokeh effects and unique perspectives
- โข Always check sign conventions: concave mirrors have positive f, convex have negative f
โ Frequently Asked Questions
What is the difference between concave and convex mirrors?
Concave mirrors curve inward and can form real or virtual images. Convex mirrors curve outward and always form virtual, diminished images. Concave mirrors converge light; convex mirrors diverge light.
How do I determine if an image is real or virtual?
Real images have positive image distance (di > 0) and form in front of the mirror where light actually converges. Virtual images have negative image distance (di < 0) and form behind the mirror where light appears to diverge from.
What happens when an object is placed at the focal point?
When do = f, the mirror equation gives di = โ, meaning the image forms at infinity. This creates parallel reflected rays, useful for collimating light sources in flashlights and headlights.
Why do convex mirrors always produce smaller images?
Convex mirrors have negative focal lengths, resulting in negative magnification magnitudes less than 1. This creates diminished images, which is why they're used in security mirrors and car side mirrors for wider viewing angles.
How is magnification related to image orientation?
Negative magnification (m < 0) indicates an inverted image, while positive magnification (m > 0) indicates an upright image. The absolute value |m| gives the size ratio relative to the object.
What is the relationship between radius of curvature and focal length?
For spherical mirrors, f = R/2 where R is the radius of curvature. The focal point is located halfway between the mirror surface and the center of curvature. This relationship holds for both concave and convex mirrors.
Can a concave mirror form a virtual image?
Yes! When an object is placed between the focal point and the mirror (do < f), a concave mirror forms a virtual, upright, magnified image behind the mirror. This is how makeup mirrors work.
๐ Official Sources
โ ๏ธ Disclaimer
This calculator provides approximate results based on the mirror equation for ideal spherical and parabolic mirrors. Real-world mirrors may exhibit aberrations, surface imperfections, and wavelength-dependent behavior. For precision optical systems, consult with optical engineers and consider advanced ray-tracing software. Results assume perfect mirror surfaces and monochromatic light unless otherwise specified.
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