Free · Ideal mechanics
Ideal Thin-Lens Projection Size
Find the thin-lens object and screen distances and the resulting projected diagonal for a real image.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
A 12.7 cm phone diagonal projected with the screen twice as far from the lens as the phone has a 25.4 cm image diagonal.
1/f=1/u+1/v; magnification=v/u; projected diagonal=phone diagonal×v/u
Worked example
Enter these known values and leave the other values blank.
- Please enter your smartphone's screen size
- 12.7 cm
- Distance between your phone and lens (u)
- 20 cm
- Distance between your lens and wall (v)
- 40 cm
- Focal length of your lens
- 13.33 cm
Assumptions and limitations
- An ideal thin converging lens forms a real image when object distance exceeds its positive focal length. Distances are measured from the lens principal plane.
- Magnification here is the positive size ratio; a real thin-lens image is inverted. The model does not predict brightness, resolution, distortion or a usable projector.
- Phone diagonal is a positive length; image diagonal scales by the same magnification as every transverse dimension. Inch and foot outputs use exact international length definitions.
- Only two of object distance, image distance and focal length are required. Clear the unknown before solving an inverse; the focal-plane singularity has no finite image distance.
Common questions
Why does moving the phone toward the focal plane enlarge the image?
For fixed focal length, v=fu/(u−f). The image distance and size ratio increase as a positive u approaches f from above.
References
Replace explanatory external images with original accessible descriptions preserving each scenario, rope or machine arrangement and every variant condition. Use exact international inch and foot factors in all seven projection presentation formulas, replacing rounded decimal conversion coefficients. Start metric phone and lens-distance controls in centimetres for the retained worked examples; display diagonal metres in metres.