MY SIMULATOR

English Lighthouse: Fresnel Lens

Prisms that bend a lamp into a beam.

INTERACTIVE 3D

Educational model of a classic rotating lens — not a navigation aid; ranges are model values, not a maritime forecast.

Lamp size

Focus error

Turn time

Lab & science

Drag to orbit, wheel / pinch to zoom. P = pause, R = reset.

Optics (same as the panel)

Setup

Lamp

Lens

Lamp height offset

Visibility (clear air = 20 km)

Ship distance

Colours

Time of day

Presets

Camera

Graphics (High on every device; Low = smaller shadows, fewer rays)

Live readout (model values)

Experiment: how big a lamp can the lens focus?

Sweeps the lamp size from 10 to 200 mm with the current focus, tracing about 4000 rays each time.

Missions

Mission 4: the glass has refractive index 1.5168. At what angle of incidence (degrees) does light inside it start to be totally reflected?

The science

What you see

A lamp at the focus of a Fresnel lens: instead of one thick glass lens the surface is cut into thin prisms. Near the axis (dioptric zones) light is refracted twice; high above and below, catadioptric prisms refract the light in, reflect it totally on the back face and refract it out. All the light that falls on the panel leaves almost horizontally. The lamp is not a point, so the beam has a width; a lens turning on its axis sweeps that beam round as a flash.

Equations

Snell                n1 sin(i) = n2 sin(t)
Critical angle       sin(ic) = 1 / n                 (about 41.3 deg for n = 1.5168)
Fresnel loss         R = (Rs + Rp)/2,  T = 1 - R      (about 4.2 % per surface at normal incidence)
Dioptric zone        tan(a) = sin(psi) / (n cos(psi') - 1),   sin(psi') = sin(psi)/n
                       (a = tilt of the outer face so that the ray leaves horizontally)
Catadioptric prism   entry face perpendicular to the ray (no bend), back face at psi/2 to the
                       horizontal: TIR turns a ray at elevation psi into a horizontal one
Paraxial lens law    exit angle = y (1/u - 1/f)       (lamp at distance u from the lens)
Beam width           FWHM ~ lamp size / f_eff          (traced here, not assumed)
Peak intensity       I = (Phi / 4 pi) (dphi / dh) p(0)     p(0): traced power per radian
Allard's law         E = I T^D / D^2   ;  visible while E >= 2e-7 lx   (T per km from the visibility)
Flash duration       t = dh / omega,   omega = 2 pi / turn time

Assumptions & honest simplifications

The ray trace is 2-D in the vertical plane (the lens is a drum of revolution); the horizontal beam width is taken as lamp size / f and each panel as a bullseye with the same optics.
Four panels, f = 0.92 m, 35 prisms per half; real lenses have other orders and more, finer prisms. Prism count and sizes here are illustrative design choices.
Glass dispersion uses a Cauchy fit through crown-glass values [typical values, verify before use]. Scattering inside the glass, dirt and the lamp's own shape are ignored.
Lamp flux (100 / 1200 / 4000 lm) and the 0.2 microlux visibility threshold are typical order-of-magnitude values, not measurements of any real light. Not a navigation aid.

Independent numerical checks

Also in node: node check.js.

Sources

Standard geometric-optics treatments of refraction, total internal reflection and Fresnel equations; Augustin Fresnel's lighthouse lens principle (public domain history); Allard's law and the usual luminous-range definition. No real lighthouse, manufacturer or drawing is reproduced.

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