Lens Equation
Physics · free browser app
Move an object around a thin lens and watch the image appear.
Description
The thin-lens equation 1/f = 1/dₒ + 1/dᵢ as a living ray diagram: move the object, change the focal length and watch the image form — real or virtual, inverted or upright, enlarged or reduced. The three principal rays that construct the image graphically can be switched on, and the magnification m = −dᵢ/dₒ is computed with every move.
Both lens kinds are on board: a converging lens (f > 0) that can throw a real image onto the far side, and a diverging lens (f < 0) that always produces a virtual, upright, reduced one. Object distance and height are freely adjustable, and the essential math is collected inside the app.
Examples
The projector: between f and 2f
Place the object between one and two focal lengths in front of a converging lens: the image lands beyond 2f on the other side — real, inverted and enlarged. That is the geometry of every projector, and the reason slides go into the tray upside down.
The camera: beyond 2f
Move the object farther out than 2f and the image jumps to between f and 2f — real, inverted and reduced. A camera works exactly there: a large scene shrinks onto a small sensor.
The magnifying glass: inside f
Push the object inside the focal length and the rays behind the lens stop converging: a virtual, upright, enlarged image appears on the object's own side — watch it happen in the ray construction. That is how a magnifying glass works.