Compute concave mirror values quickly with confidence. See clear steps, magnification, and image type instantly. Save CSV or PDF, and keep your records safe.
| # | f | do | di (computed) | m | Notes |
|---|---|---|---|---|---|
| 1 | 10 cm | 30 cm | 15 cm | -0.50 | Real, inverted, reduced |
| 2 | 12 cm | 24 cm | 24 cm | -1.00 | Real, inverted, same size |
| 3 | 8 cm | 12 cm | 24 cm | -2.00 | Real, inverted, enlarged |
| 4 | 10 cm | 10 cm | ∞ | — | Object at focus, image at infinity |
The calculator uses the mirror equation: 1/f = 1/do + 1/di. Provide signed distances using one consistent convention.
The mirror equation links focal length f, object distance do, and image distance di. When do is larger than f, a real image usually forms in front of the mirror. When do is smaller than f, the image often becomes virtual and appears behind the mirror.
Many lab setups use focal lengths between 5 cm and 20 cm. Common object distances are 15 cm, 20 cm, 30 cm, and 40 cm because they fit on a meter stick. For example, with f = 10 cm and do = 30 cm, the computed image distance is about di = 15 cm.
Magnification is m = −di/do. If |m| < 1, the image is reduced; if |m| > 1, it is enlarged. The sign helps: negative m indicates an inverted image, while positive m indicates an upright image.
When the object is placed at the focal distance (do = f), the term 1/f − 1/do becomes zero. That makes di approach infinity, meaning rays leave parallel and the image is effectively “at infinity.”
A spherical concave mirror has R = 2f. So a mirror with f = 12 cm has R = 24 cm. If you know the mirror’s curvature from a spec sheet, this relation helps verify whether your computed focal length is reasonable.
Textbooks differ, so this calculator accepts signed values. A common convention sets real images with positive di and virtual images with negative di. Choose one convention and keep it for f, do, and di to avoid contradictory results.
Measure distances from the mirror’s vertex (the center of the reflective surface). Keep the object near the principal axis to reduce aberrations. If your measured di varies by a few millimeters, the computed magnification can shift noticeably when do is close to f.
The example row f = 8 cm and do = 12 cm yields di = 24 cm and m = −2. That matches the expectation of a real, inverted, enlarged image. Use these benchmarks to spot input or sign errors quickly.
No. You need two of the three values: f, do, and di. The mirror equation requires two known terms to compute the unknown one reliably.
This happens when do equals f. The math makes 1/di go to zero, so rays become parallel and the image is effectively at infinity.
Negative m indicates an inverted image under the chosen sign convention. The magnitude |m| tells you the size ratio, such as |m|=2 meaning twice as tall.
Not necessarily. A negative di often represents a virtual image located behind the mirror, which can occur when the object is inside the focal length.
No. You can use mm, cm, meters, or inches. Just keep every distance in the same unit. The calculator labels outputs using the unit you select.
Rounding changes the displayed numbers and step text. Use 3–5 digits for most homework. When do is close to f, small rounding can noticeably affect di.
Because R = 2f is a standard mirror property. It helps you cross-check mirror specs and ensures your computed focal length matches the physical curvature of the mirror.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.