Example data table
| Mirror | f (cm) | do (cm) | di (cm) | m | Image |
|---|---|---|---|---|---|
| Concave | +10 | +30 | +15 | -0.5 | Real, inverted, reduced |
| Concave | +10 | +15 | +30 | -2 | Real, inverted, enlarged |
| Concave | +10 | +8 | -40 | +5 | Virtual, upright, enlarged |
| Convex | -12 | +30 | -8.571 | +0.286 | Virtual, upright, reduced |
| Convex | -20 | +50 | -14.286 | +0.286 | Virtual, upright, reduced |
Formulas used
- Mirror equation: 1/f = 1/do + 1/di
- Magnification: m = -di/do and m = hi/ho
- Radius of curvature: R = 2f (spherical mirror)
How to use this calculator
- Select your preferred unit.
- Choose mirror type and decide whether to auto-sign f.
- Pick what to solve in the mirror equation and enter the other two values.
- Pick what to solve in magnification and enter the required values.
- Press Calculate to view results above the form.
- Use Download CSV or Download PDF to export.
Mirror optics mini‑guide
1) The mirror equation in real setups
A spherical mirror links focal length f, object distance do, and image distance di using 1/f = 1/do + 1/di. If do is much larger than f, then di approaches f.
2) Signed distance conventions that matter
This calculator supports signed distances. A common convention is do > 0 for an object in front of the mirror. Concave mirrors use f > 0, while convex mirrors use f < 0. A real image forms in front, so di > 0; a virtual image appears behind, so di < 0.
3) Concave mirror data you can expect
With a concave mirror, placing the object beyond the focal length often produces a real, inverted image. For example, f=+10 cm and do=+30 cm gives di=+15 cm and m=-0.5. Moving the object closer, do=+15 cm yields di=+30 cm and m=-2, so the image is larger. At do=2f, di=2f and m=-1 exactly.
4) Convex mirrors and why images look smaller
A convex mirror produces a virtual, upright, reduced image for most real objects. Using f=-12 cm and do=+30 cm gives di≈-8.571 cm and m≈+0.286. That positive magnification matches an upright image, and the small magnitude explains the reduced size.
5) Magnification connects distance and height
Magnification can be computed from distances m=-di/do or from heights m=hi/ho. If ho=5 cm and m=-0.5, then hi=-2.5 cm, which indicates an inverted image. Use the sign of hi to track orientation.
6) Radius of curvature and quick checks
For a spherical mirror, R=2f. So a concave mirror with f=+10 cm has R=+20 cm. This is a typical fast sanity check when you measure curvature directly. In labs, mirrors have |f| between 5 and 50 cm, depending on curvature.
7) Infinity cases and parallel rays
When do equals f, the denominator (1/f − 1/do) approaches zero, so di tends to infinity. Practically, the reflected rays become nearly parallel, which is why a source at the focal point can create a collimated beam.
8) Practical tips for cleaner results
Keep one unit across all lengths and match rounding to your measurements. If you know the mirror type but entered an unsigned f, enable auto‑sign to reduce mistakes. Compare “Image Type” and “Orientation” to confirm your sign choices.
FAQs
1) What if I only know the focal length and object distance?
Set the mirror solve option to di, then enter f and do. The calculator computes di and derives m when possible.
2) Why is my image distance negative?
Negative di indicates a virtual image that appears behind the mirror. This is common for convex mirrors, and also for concave mirrors when the object is inside the focal length.
3) What does a negative magnification mean?
A negative magnification means the image is inverted relative to the object. The magnitude |m| tells size change: above 1 is enlarged, below 1 is reduced.
4) Can I compute image height without distances?
Yes. Choose the magnification solve option as hi, then enter m and ho. The calculator uses hi = m·ho.
5) What should I enter for a convex mirror focal length?
Use a negative focal length in the common sign convention. If you only have the magnitude, enable auto‑sign and select “Convex” so the calculator applies the negative sign.
6) Why does the calculator mention infinity?
If do is equal to f, the computed di tends to infinity. That corresponds to nearly parallel reflected rays, a standard optics edge case.
7) Which inputs are best for avoiding sign errors?
Enter do positive for real objects in front. Use f>0 for concave and f<0 for convex. Then verify “Image Type” to confirm the sign of di.