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Smartphone Projector Lens Geometry Calculator — result sheet
Estimate screen distance, signed magnification, projected image height, and orientation from a thin-lens smartphone projector geometry.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For a real image, image distance = focal length × object distance ÷ (object distance − focal length); signed magnification = −image distance ÷ object distance; projected height = absolute magnification × object height.
A simple phone projector uses a lens to form a real image on a screen. This page applies the thin-lens equation and magnification relation, reports the screen distance and image scale, and makes inversion visible. It does not model brightness, distortion, alignment, or a finished projector’s performance.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Lens focal length — mm; minimum 1.0E-6; maximum 1000000
- Phone display to lens distance — mm; minimum 1.0E-6; maximum 1000000
- Displayed object height — mm; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Lens focal length | 50 |
| Phone display to lens distance | 60 |
| Displayed object height | 10 |
A 50 mm lens with a 60 mm object distance forms an image 300 mm away with signed magnification −5 and a 50 mm image-height magnitude.
Assumptions and limits
- The lens is treated as a thin converging lens with a positive focal length.
- The display is farther from the lens than the focal length so a real image can form.
- Object and image distances use the same millimetre unit.
- The image-height result is a geometric magnitude; the negative magnification indicates inversion.
- Lens thickness, aberrations, aperture, keystone, focus tolerance, and screen properties are omitted.
- The result is an optical geometry estimate, not a construction or eye-safety instruction.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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