Concave Mirror Equation Calculator

Compute concave mirror values quickly with confidence. See clear steps, magnification, and image type instantly. Save CSV or PDF, and keep your records safe.

Calculator

Leave the solved value blank or ignored.
All distances must use the same unit.
Controls rounding in outputs and steps.
Concave often uses positive f in many texts.
Use your chosen sign convention consistently.
Real images usually give positive di.
If provided, hi = m·ho is reported.
Reset

Example data table

# 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

Formula used

The calculator uses the mirror equation: 1/f = 1/do + 1/di. Provide signed distances using one consistent convention.

How to use this calculator

  1. Select what you want to solve for: di, do, or f.
  2. Enter the other two signed values, using one unit.
  3. Optionally enter object height to get image height.
  4. Click Calculate to see results above the form.
  5. Use Download CSV or Download PDF to save outputs.

Concave mirror guide

1) What the mirror equation tells you

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.

2) Typical distance ranges in classroom problems

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.

3) Using magnification to predict size

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.

4) The special case at the focal point

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.”

5) Radius of curvature gives a quick check

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.

6) Sign conventions and consistent inputs

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.

7) Practical measurement tips

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.

8) How to use the example table as a benchmark

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.

FAQs

1) Can I solve for focal length if I only know one distance?

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.

2) Why does the calculator show infinity for image distance?

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.

3) What does a negative magnification mean?

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.

4) Is a negative image distance always wrong?

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.

5) Do I have to use centimeters?

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.

6) How accurate are the results if I round heavily?

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.

7) Why include radius of curvature in a mirror calculator?

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.

Note: This tool supports signed conventions, but conventions vary by textbook. If your class uses a different sign rule, enter values accordingly.

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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.