A shoebox, a magnifying glass and a phone make a simple projector. The phone must sit just outside the lens’s focal length to throw a large, sharp, inverted image onto a wall.
How to use the Smartphone Projector Calculator
- Lens focal length f
- Phone-to-lens distance u
- Phone screen diagonal
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the lens focal length, the phone-to-lens distance and the phone’s screen diagonal.
Inputs explained
| Field | What to enter |
|---|---|
| Lens focal length f | Units: cm, mm, m, in, ft |
| Phone-to-lens distance u | Units: cm, mm, m, in, ft |
| Phone screen diagonal | Units: in, cm |
What each result means
- Magnification = [Lens-to-wall distance for a sharp image]÷[Phone-to-lens distance u]
- Projected image diagonal = [Magnification]×[Phone screen diagonal]
Formula
1/f = 1/u + 1/v, M = v/u, image size = M × screen size
Worked example
Inputs — Lens focal length f: 20 cm; Phone-to-lens distance u: 22 cm; Phone screen diagonal: 6.1 in.
Results — Lens-to-wall distance for a sharp image = 2.2 m; Magnification = 10 ×; Projected image diagonal = 61 in; Setup = Real image – it works.
Key terms
- Real image
- Image formed where light rays actually converge.
Frequently asked questions
Why is the image upside down?
A single convex lens forms an inverted real image – lock your phone's rotation and flip it.
How do I get a bigger picture?
Move the phone closer to the focal point and the wall farther away.
Why is it dim?
Light spreads over a large area; use a dark room and maximum brightness.
What lens works best?
A large-diameter magnifier with a focal length of 15–30 cm.