Calculator Inputs
Leave exactly one of the first three distance fields blank to solve it. Use positive and negative signs according to the thin lens sign convention.
Plotly Graph
This graph shows how image distance changes as object distance varies for the solved or supplied focal length.
Example Data Table
| Case | Focal Length (cm) | Object Distance (cm) | Image Distance (cm) | Magnification | Interpretation |
|---|---|---|---|---|---|
| 1 | 10 | 30 | 15 | -0.50 | Real, inverted, reduced |
| 2 | 10 | 15 | 30 | -2.00 | Real, inverted, enlarged |
| 3 | 10 | 8 | -40 | 5.00 | Virtual, upright, enlarged |
| 4 | -10 | 30 | -7.5 | 0.25 | Virtual, upright, reduced |
Formula Used
Thin lens equation:
1 / f = 1 / do + 1 / di
Magnification:
m = - di / do
Image height:
hi = m × ho
Optical power:
P = 1 / f in diopters when f is in meters.
- f > 0 for a converging lens, and f < 0 for a diverging lens.
- do > 0 for a real object placed before the lens.
- di > 0 for a real image, and di < 0 for a virtual image.
- m > 0 means upright, and m < 0 means inverted.
How to Use This Calculator
- Select the distance unit for focal length, object distance, and image distance.
- Enter any two of the three core distance values and leave one blank.
- Optionally enter object height to calculate image height.
- Choose the decimal precision and graph range multiplier.
- Press Calculate to view results, classification, graph, and download options.
FAQs
1. What does the thin lens equation calculate?
It relates focal length, object distance, and image distance for an ideal thin lens. When two values are known, the third can be solved directly.
2. Why should one field stay blank?
The calculator solves one missing variable from the other two. Leaving more than one blank makes the problem underdefined and prevents a unique solution.
3. What sign should I use for focal length?
Use a positive focal length for converging lenses and a negative focal length for diverging lenses. This keeps the equation consistent with standard optics sign conventions.
4. How do I know whether the image is real or virtual?
A positive image distance indicates a real image. A negative image distance indicates a virtual image. The result panel labels this automatically after calculation.
5. What does magnification tell me?
Magnification compares image size with object size. Negative magnification means the image is inverted, while positive magnification means it is upright.
6. Can this calculator handle diverging lenses?
Yes. Enter a negative focal length for a diverging lens. The calculator will still determine image distance, magnification, and image classification correctly.
7. Why is the image distance sometimes extremely large?
When the object distance approaches the focal length, the denominator in the lens equation becomes very small. That makes the computed image distance grow very large.
8. What do the CSV and PDF downloads contain?
They export the result summary, including solved distances, magnification, optical power, lens classification, and consistency notes for quick sharing or recordkeeping.