Thin Lens Equation Calculator
Use the thin-lens relationship for an idealised real object and real image with positive distance magnitudes. The tool reports focal-length magnitude and magnification magnitude.
How to use this calculator
- Enter the object distance (cm) using the units shown beside the field.
- Enter the image distance (cm) using the units shown beside the field.
- Review the calculated values and check that the assumptions match your scenario.
- Change one input at a time when comparing scenarios so you can see which assumption drives the result.
Formula and assumptions
Thin lens focal length f = (object distance × image distance) / (object distance + image distance); magnitude of lateral magnification = image distance / object distance.
- Sign conventions, lens thickness, aberrations and virtual images require the appropriate optical model; this tool uses positive distances for the stated case.
- The result is computed from the values you provide; it does not fetch external rates, live account data or local rules.
Worked examples
Worked example
Object distance 30 cm and image distance 15 cm gives a focal length of 10 cm and magnification magnitude 0.5×.
Example inputs: Object distance (cm) = 30, Image distance (cm) = 15.
Compare the displayed output with your own measurements before using it in a decision.
Understanding the result
Sign conventions, lens thickness, aberrations and virtual images require the appropriate optical model; this tool uses positive distances for the stated case.
Results are estimates based on the stated model. If the situation depends on measured conditions or contractual specifications, use those source values rather than typical assumptions.
Important notes
Sign conventions, lens thickness, aberrations and virtual images require the appropriate optical model; this tool uses positive distances for the stated case.
Frequently asked questions
What formula does this calculator use?
It uses the method described above: Thin lens focal length f = (object distance × image distance) / (object distance + image distance); magnitude of lateral magnification = image distance / object distance.
What should I verify before relying on the result?
Sign conventions, lens thickness, aberrations and virtual images require the appropriate optical model; this tool uses positive distances for the stated case.
Can I compare different scenarios?
Yes. Change the inputs while keeping units and definitions consistent, and record the assumptions used for each scenario.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.