What you are looking at
A convex lens (thicker in the middle) sits in the centre on a horizontal line called the axis. The marks labelled F are its focal points, one focal length away on each side; 2F marks twice that distance. The white arrow on the left is an object, and light leaves its tip in every direction.
Three rays are easy to follow, and any two of them are enough to find the image:
- A ray travelling parallel to the axis bends through the focal point on the far side.
- A ray through the very centre of the lens goes straight on.
- A ray through the near focal point leaves the lens parallel to the axis.
Where those rays meet, the lens forms an image of the tip of the arrow.
What changes as the object moves
- Far away: a small, upside-down image just beyond the far focal point. A camera works like this.
- At 2F: the image is the same size as the object and just as far away, upside down.
- Between F and 2F: the image grows and moves further away. A projector works like this.
- At F: the rays leave parallel and never meet, so there is no image.
- Inside F: the rays spread apart. Traced backwards (the dashed lines), they seem to come from a larger, upright image on the same side as the object. Nothing actually gathers there, which is why it is called a virtual image. A magnifying glass works like this.
The rule behind it
For a thin lens, 1/f = 1/do + 1/di, where f is the focal length, do the distance to the object and di the distance to the image. The image's size compared with the object is -di/do; a negative size means upside down. The readout at the top of the piece shows these numbers as they change.
What this leaves out
This is a simplified model: a perfectly thin lens, light of one colour, and no blur at the edges. Real lenses bend different colours slightly differently and are not perfectly thin, which is why camera lenses are built from several pieces of glass.
Try it
Switch to Play and drag the object distance slowly from 9 down to 0.6. Then make the lens stronger (a shorter focal length) and notice how everything moves closer.