Physics·Optics

Ray Optics Simulator — Thin Lens

Move the object, swap between convex and concave, change the focal length. See the image form via three principal rays.

u = 180 px

v = 225 px

m = -1.25

Real, inverted

Object distance180pxObject height60pxFocal length |f|100px

The thin-lens equation predicts where an image forms and how large it is, given an object's position and the lens's focal length. This simulator draws the three principal rays for you — the parallel-then-through-focus ray, the through-center ray, and the through-focus-then-parallel ray — and shows where they converge (or appear to diverge from) to form the image. Drag the object left-right, or the object arrowhead up-down. Toggle between convex and concave lenses. Move the focal-length slider to see how the image changes.

Key equations

Thin lens equation

$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$

Linear magnification

$m = \dfrac{v}{u} = \dfrac{h'}{h}$

Sign convention (Cartesian)

$\text{Distances measured from lens; against light} < 0, \text{along light} > 0$

Key ideas to remember

1
For a real object in front of a convex lens: object beyond $2f$ → real, inverted, smaller image between $f$ and $2f$ .
2
Object at $f$ → image at infinity (rays emerge parallel).
3
Object between $f$ and lens → virtual, upright, magnified image on the same side as the object.
4
Concave lens always makes a virtual, upright, diminished image regardless of object position.

Ray Optics Simulator — Thin Lens

Key equations

Key ideas to remember

Related topics

Solve optics problems on RankGrind

Personalized Learning

Concept Mastery

Smart Practice

Daily Challenges