Geometric Optics

Place an object in front of a thin lens. Drag it or use the sliders, change the focal length, and follow the three principal rays to find where the image forms, how big it is, and whether it is real or virtual.

Speed

How the model works

A thin lens obeys the lens equation (real-is-positive convention):

1/f = 1/d_o + 1/d_i, m = −d_i / d_o

f > 0 for a converging (convex) lens and f < 0 for a diverging (concave) lens.
d_i > 0 means a real image on the far side, which can be shown on a screen. d_i < 0 means a virtual image on the object's side.
m < 0 means the image is inverted.

Three principal rays locate the image: (1) parallel to the axis, then through the far focal point; (2) through the centre of the lens, undeviated; (3) through the near focal point, then parallel. Dashed lines are extensions back to a virtual image.

Paraxial thin-lens model: no thickness, no aberrations, rays close to the axis. Distances in centimetres.

Guided experiments

Object at 2f. f = 10 cm, object at 20 cm. Prediction: a real, inverted image at 20 cm on the other side, the same size (m = −1).
Magnifying glass. Move the object inside f, to 6 cm. Prediction: a virtual, upright, enlarged image (m = 2.5) on the same side as the object. The rays diverge, so their extensions meet.
Diverging lens. f = −10 cm, object at 20 cm. Prediction: always virtual, upright and smaller. Here d_i = −6.67 cm and m = 0.33.

Challenge

A projector lens (f = 5 cm) must throw a sharp image onto a screen 3 m away. How far from the lens should the slide be, and how big is a 2 cm feature on the screen?

Reveal the explanation

1/d_o = 1/5 − 1/300, so d_o ≈ 5.085 cm, just outside f. Magnification m = −300/5.085 ≈ −59, so a 2 cm feature is about 1.18 m tall and inverted. That is why slides go into projectors upside down.

References

OpenStax, University Physics Volume 3, §2.4 “Thin Lenses”.