Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Educators · Gaussian Beam

Gaussian Beam for a mirage

Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate a mirage live below — adjust the inputs and watch it respond, right in your browser.

Gaussian BeamLive

how a laser beam spreads

Controls

Presets

Beam waist w₀ (µm)

Wavelength (nm)

A real laser beam is not a perfect ray — it narrows to a minimum waist then spreads. Within one Rayleigh range of the waist it stays roughly collimated; beyond, it diverges at an angle set by wavelength over waist size. Tighter focus means faster spreading — the fundamental diffraction trade-off behind every laser and telescope.

▶ Run in Python

Data Inspector

Rayleigh range0.012 m

Divergence4.03 mrad

Waist50 µm

Governing equation

w (z) = w_{0} 1 + (z / z_{R})^{2}, z_{R} = \frac{π w _{0}^{2}}{λ} = 12.4 mm

Reading this result: Divergence is set by λ/(π·w₀): shrinking the waist or lengthening the wavelength both make the beam spread faster — the core diffraction trade-off.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Students Researchers Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Gaussian Beam

Gaussian Beam for a camera lens Gaussian Beam for a laser beam Gaussian Beam for a fiber-optic cable Gaussian Beam for a microscope Gaussian Beam for a telescope Gaussian Beam for a prism Gaussian Beam for a rainbow Gaussian Beam for a hologram

Frequently asked questions

Is this good for educators?: Yes — this version of "Gaussian Beam for a mirage" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.