MY SIMULATOR

Polarizer Bench: Malus & Brewster

Rotate the filters and watch the light.

INTERACTIVE 3D

Educational model with an idealised LED and a low-power detector — no real laser is involved; values are model values.

Filter 1

Filter 2

Filter 3

Lab & science

Drag to orbit, wheel / pinch to zoom. P = pause, R = reset, M = mode. Angles are measured from vertical.

Graphs (same as the panel)

Setup

Light source

Filter quality (typical order-of-magnitude values)

Reflecting plate material (glare mode)

Presets

Camera

Graphics (High on every device; Low = smaller shadows, lower pixel ratio)

Live readout (model values)

Experiments

1. Ideal filters at 0° and 90°, middle filter swept 0°-180° in 1° steps. 2. Glare plate swept in 0.01° steps to find where p-light disappears.

Missions

Mission 5: at what angle of incidence (degrees) is light reflected from water (n = 1.333) completely polarised? Enter a number.

The science

What you see

Light is a transverse wave: its electric field wiggles in a plane. A polarising filter only lets the part of the field along its transmission axis through. An LED is unpolarised (the plane changes randomly), so a filter passes half of it and the light that comes out is polarised along the axis. The cyan wave in the beam is that plane of vibration, its height is the field amplitude. In glare mode a clear plate reflects mostly light polarised parallel to its surface; at one special angle (Brewster) the other polarisation is not reflected at all.

Equations

Malus' law           I = I0 cos^2(theta)          (polarised light, ideal analyser)
Unpolarised light    I = I0 / 2 after the first ideal filter
Three filters        I = (I0/8) sin^2(2 theta)    (0 deg, theta, 90 deg; I0 = unpolarised input)
Stokes vector        S = (I, Q, U, V);  Q = I_vertical - I_horizontal;  S_out = M(theta) S_in
Filter (Mueller)     M = 1/2 [ T1+T2 , (T1-T2)c , (T1-T2)s , 0 ;
                               (T1-T2)c , (T1+T2)c^2 + 2g s^2 , (T1+T2-2g) c s , 0 ;
                               (T1-T2)s , (T1+T2-2g) c s , (T1+T2)s^2 + 2g c^2 , 0 ;  0,0,0, 2g ]
                     c = cos 2theta, s = sin 2theta, g = sqrt(T1 T2)
Fresnel              rs = (n1 cos i - n2 cos t)/(n1 cos i + n2 cos t),   rp = (n2 cos i - n1 cos t)/(n2 cos i + n1 cos t)
Snell                n1 sin i = n2 sin t ;  Rs = rs^2 ,  Rp = rp^2
Brewster angle       tan(theta_B) = n2 / n1       (Rp = 0 ; i + t = 90 deg)
Degree of pol.       DOP = sqrt(Q^2 + U^2 + V^2) / I

Assumptions & honest simplifications

The beam is treated as a perfectly collimated, monochromatic ray bundle; no interference between filters or in the plate, no diffraction, no filter dispersion or wavelength dependence.
Filter presets use principal transmittances T1 (along the axis) and T2 (across it): ideal 1 / 0, "good film" 0.85 / 0.0005, "cheap film" 0.75 / 0.02. These are typical order-of-magnitude values for dichroic sheet filters, not measurements of any product.
Glare mode uses one air-to-plate surface only; the rear surface reflection (a second, weaker beam) and absorption are left out. Refractive indices are typical visible-light values.
Source power (10 mW) and the meter scale are illustrative. The detector is linear and has no noise.

Independent numerical checks

Also in node: node check.js.

Sources

Standard treatments of Malus' law (E. L. Malus, 1809), Brewster's angle (D. Brewster, 1815), Fresnel's equations and the Stokes-Mueller formalism (e.g. Hecht, Optics; Chipman's Mueller matrices for polarisers). All public-domain physics; no products or brands are modelled.

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