Smartphone Projector Calculator

A single converging lens projects a magnified image of a phone screen onto a wall.

How the Math Works

The Smartphone Projector Calculator uses the lens formula 1/f = 1/d_o + 1/d_i to determine the relationship between a lens's focal length (f), the object distance (d_o), and the image distance (d_i). This formula calculates where the projected image will form relative to the lens. Once these distances are known, magnification (M) is found by dividing the image distance by the object distance (M = d_i ÷ d_o), revealing how much larger the projected image appears compared to the original object.

Practical Applications

To apply this calculation, first measure or estimate the focal length of your lens and position your smartphone (the object) at a known distance (d_o) from the lens. Plug these values into the formula to solve for d_i, the distance where the image will form. Then, divide d_i by d_o to find the magnification. This tells you where to place your projection screen for optimal focus and how large the image will appear, enabling precise adjustments for your DIY projector setup.

Day-to-Day Use

This calculation empowers everyday creativity, such as building a smartphone projector for movie nights or presentations without buying expensive equipment. By understanding magnification, you can tweak your setup to project larger images onto walls or screens, making impromptu home theaters or educational demonstrations possible. It also helps troubleshoot common issues like blurry or distorted projections by guiding adjustments to lens placement or object distance, turning a simple smartphone into a versatile visual tool.

Worked example

100 mm lens, phone at 150 mm → image at 300 mm, 2× magnification.

FAQ