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The law of reflection states that the angle of incidence equals the angle of reflection. Curved mirrors focus parallel rays to a focal point (concave) or appear to diverge from one (convex). Parabolic mirrors eliminate spherical aberration.
When light crosses a boundary between media: n1 sin ฮธ1 = n2 sin ฮธ2. Glass (n โ 1.5) bends light toward the normal on entry. When the internal angle exceeds the critical angle, total internal reflection occurs.
At every interface, some light reflects and some transmits. The Fresnel equations give the exact ratio depending on angle and polarization. At normal incidence on glass, about 4% reflects. At grazing angles, reflection approaches 100%.
Refractive index varies with wavelength: n(ฮป) = A + B/ฮปยฒ (Cauchy equation). Shorter wavelengths (blue/violet) bend more than longer ones (red). A prism separates white light into a spectrum. This is chromatic dispersion.
For ideal lenses: 1/f = 1/v โ 1/u, where f is focal length, v is image distance, u is object distance. Converging lenses (f > 0) form real images when the object is beyond the focal point. The simulator's ideal lens uses this equation directly.
A grating with line spacing d diffracts light according to d(sin ฮธout โ sin ฮธin) = mฮป, where m is the order number. Different wavelengths diffract to different angles, producing a spectrum similar to a prism but with sharper separation.
Use this Ray Optics Simulator: choose a preset or add optical elements (mirrors, lenses, prisms, beam splitters) from the toolbar. Drag objects to position them and the simulator traces rays in real time using Snell's law. No download or signup needed.
TIR occurs when light travels from a denser medium (glass, n=1.5) to a less dense medium (air, n=1) at an angle exceeding the critical angle, arcsin(n2/n1). Beyond this angle, 100% of light reflects. Try it with the Glass Slab or Prism presets.
Different wavelengths bend by different amounts (dispersion). Red bends less, violet bends more. When white light enters a prism, Snell's law with wavelength-dependent refractive index separates the colors. Load the "Prism Rainbow" preset to see this.
Fresnel equations calculate reflected vs. transmitted light fractions at an interface. Enable the "Fresnel" toggle in the controls row to see partial reflections at glass surfaces โ some light reflects while the rest transmits, with brightness proportional to the Fresnel coefficients.
19 elements: sources (point, parallel beam, single ray), mirrors (flat, curved, parabolic, ideal), refractors (glass slab, prism, circle lens, spherical lens, ideal lens), beam splitter (with dichroic option), diffraction grating, GRIN lens, blockers (flat, aperture, circle), and observer.
Yes. Load the Telescope preset for a two-lens refracting telescope. For a microscope, place two converging lenses with appropriate focal lengths and spacing. Add light sources and apertures to complete the optical system.
GRIN (Gradient-Index) lenses have a refractive index that varies across the material, typically decreasing from center to edge. This bends rays continuously inside the lens without curved surfaces. The simulator uses Euler step integration to trace rays through GRIN media.
Yes, completely free with no signup. Runs entirely in your browser. Ideal for physics courses covering geometric optics. Students can experiment with presets and build custom scenes. Teachers can export as PNG for presentations and worksheets.
Sequential multi-surface lens design with Sellmeier materials, spot diagrams, ABCD matrix, and chromatic aberration analysis.
Single lens focal length from R1, R2, and refractive index. Combined and double lens systems.
Refraction calculator with Snell's law, critical angle, prism deviation, and interactive diagrams.