idle↑PrevNext↓↓ scroll for more sims▲35▼Polarization — Malus's Law and the 3-Filter Paradox☆r/optics·u/matrix·3 comments·link🖱drag filters to rotate themUnpolarized light from a lamp travels through 1, 2, or 3 linear polarizing filters whose transmission axes you can rotate by dragging. The first filter halves the intensity and polarizes the beam; each subsequent filter applies Malus's law, I′=Icos2(Δθ), where Δθ is the angle between successive axes. With two filters at 0° and 90° the output drops to zero — crossed polarizers fully extinguish the light. Now insert a third filter between them at 45°: instead of staying dark, the detector lights up to I=21⋅21⋅21=81 of the source. Adding an absorber makes the beam brighter — the classic 3-polarizer 'paradox' that exposes how a polarizer projects rather than merely blocks. Drag the pin or the body of any filter to rotate; use the 1/2/3 buttons to toggle the count.show more
pausedidle↑PrevNext↓▲28▼Snell's Law and Total Internal Reflection☆r/optics·u/matrix·1 comment·link🖱drag the laser; tap n1/n2 to change mediaRefraction at a flat interface between two transparent media follows n1sinθ1=n2sinθ2. Drag the white source to change the angle of incidence and watch the red incident, orange reflected, and cyan refracted rays update with their angles labeled. Cycle each medium through air, water, glass, and diamond using the on-canvas buttons; when n1>n2 and θ1 exceeds θc=arcsin(n2/n1), the refracted ray vanishes and you see total internal reflection.show more
pausedidle↑PrevNext↓▲18▼Concave Mirror: Principal Rays☆r/optics·u/matrix·3 comments·link🖱drag the objectRay-construction for a concave spherical mirror. The mirror's pole P sits on the right; the focal point F is at distance f to the left and the center of curvature C at 2f (since R=2f in the paraxial limit). From the tip of the object arrow three principal rays are drawn: one parallel to the axis that reflects through F, one through F that reflects parallel to the axis, and one through C that reflects straight back along itself. They converge on the image predicted by the mirror equation u1+v1=f1, with magnification M=−v/u. Drag the green object arrow: with u>f the image is real and inverted on the same side as the object; bring the object inside f and the reflected rays diverge, so a virtual upright image appears behind the mirror (shown via dashed back-traced rays).show more
pausedidle↑PrevNext↓▲17▼Snell's Window☆r/optics·u/matrix·2 comments·linkLook up from beneath a calm water surface and the entire above-water hemisphere is squeezed by refraction into a single bright disk overhead — Snell's window. Its half-angle is the critical angle θc=arcsin(1/nwater)≈48.6∘, so the full cone spans about 97∘. Outside that cone the surface acts as a mirror by total internal reflection and you see the seabed (a swimming fish and sandy caustics) flipped above you. Pixel radius inside the disk maps linearly to the underwater angle θ2, which Snell's law nwatersinθ2=sinθ1 unbends to the real sky angle θ1; the rim corresponds to light grazing the surface at θ1=90∘. Ripples warp the boundary and shimmer the sun.show more
pausedidle↑PrevNext↓▲7▼Young's Double-Slit Interference☆r/optics·u/matrix·2 comments·link🖱top half: wavelength · bottom half: slit spacingCoherent light from a point source illuminates a barrier with two slits separated by d, producing the classic fringe pattern I(θ)=cos2(πdsinθ/λ) on the screen below. The top half shows geometry — wavefronts, Huygens wavelets from each slit, and a thin colored strip of the live pattern — while the bottom half plots the cos^2 intensity curve with bright-fringe order markers m=0,±1,±2,… Color tracks the wavelength across the visible spectrum (violet at small λ, red at large λ). Watch the fringe spacing Δx≈λL/d widen as you shrink d or stretch λ.show more
pausedidle↑PrevNext↓▲2▼Thin Lens: Principal Rays☆r/optics·u/matrix·2 comments·link🖱drag the objectRay-construction for a thin converging lens. From the tip of the object three principal rays are drawn: one parallel to the axis that bends through the far focal point F′, one straight through the lens center, and one through the near focal point F that emerges parallel. They converge to the image predicted by the thin-lens equation v1=f1−u1, with magnification M=−v/u. Drag the object freely: when it sits beyond f you get a real inverted image on the far side; bring it inside f and the outgoing rays diverge, so a virtual upright image appears on the object's side (shown via dashed back-traced rays). Click near either F marker and drag to retune the focal length.show more
pausedidle↑PrevNext↓▲7▼Single-Slit Diffraction: sinc² Pattern☆r/optics·u/matrix·1 comment·link🖱top half of canvas scrubs wavelength, bottom half scrubs slit width (desktop: hold Shift to force wavelength)Fraunhofer single-slit diffraction. A plane wave hits an aperture of width a; Huygens wavelets from points across the slit interfere on a distant screen to produce the intensity pattern I(θ)=I0sinc2(πasinθ/λ). The central maximum dominates, flanked by side lobes that fade rapidly, with the first minimum at θ1=arcsin(λ/a). Move the cursor in the top half of the canvas to scrub the wavelength λ; move it in the bottom half to scrub the slit width a. Desktop users can also hold Shift to force wavelength scrubbing. Dashed orange lines mark θ1 on the screen.show more
pausedidle↑PrevNext↓▲7▼Prism: White Light to Rainbow☆r/optics·u/matrix·2 comments·link🖱drag incident ray angleA triangular glass prism splits white light into its spectrum by dispersion. Each wavelength refracts at both prism faces with a slightly different index, modeled by the Cauchy approximation n(λ)=A+B/λ2 with A≈1.50 and an exaggerated B so the fan is visible. Twenty-four sampled wavelengths from 400 nm (violet) to 700 nm (red) are traced through the prism with Snell's law at entry and exit, producing the classic rainbow fan on the far side — violet bends most, red bends least. Drag the white source dot to change the incident ray angle and watch the angle of minimum deviation pass through.show more