Snell's Law · Critical angle · Numerical Aperture · V-number · Single vs multi-mode
Light confined inside a glass core by total internal reflection — no mirrors, no metal, just Snell's law at a glass-glass interface. This simulation lets you explore every key optical fiber parameter in real time.
When light hits the core-cladding boundary at an angle greater than the critical angle θc = arcsin(n2/n1), 100% of the energy reflects back. The numerical aperture NA = √(n1²−n2²) defines the cone of angles that can enter and be guided. The V-number V = πdNA/λ determines how many modes fit: single-mode fibers (V < 2.405) carry one electromagnetic mode, eliminating modal dispersion and allowing Tbit/s data rates over thousands of kilometres.
Use the preset buttons to switch between single-mode (thin core, small index difference) and multi-mode (large core, many bouncing rays). Drag the Core RI slider above the Cladding RI — when they are close the acceptance cone narrows and fewer rays are guided. Watch the V-number: when it drops below 2.405 only one ray path survives. The acceptance angle shows the maximum tilt from the axis at which you can shine a light source into the fiber.
The global internet runs on optical fiber — a single hair-thin glass strand carries over 100 Tbit/s. Fiber optics were commercially deployed in 1977; today there are over 1 billion km of installed fiber worldwide — enough to circle the Earth 25 000 times. Medical endoscopes use bundles of thousands of fibers so surgeons can see inside the body without open surgery. The 2009 Nobel Prize in Physics was awarded to Charles Kao for his pioneering work on light transmission in optical fibers.
This simulation renders a side view of a step-index optical fibre using a GLSL fragment shader. Light launched into the high-index core (n₁) zig-zags along the fibre by total internal reflection, which occurs whenever a ray strikes the core–cladding wall at an angle of incidence beyond the critical angle, given by θc = arcsin(n₂/n₁). Rays that exceed the fibre's acceptance limit fail to reflect and leak into the lower-index cladding.
The Core RI and Cladding RI sliders set the two refractive indices (n₁ is held above n₂), the launch-angle slider tilts the entering rays from the fibre axis, and the input-rays slider adds more pulses to illustrate multi-mode behaviour. Live readouts show the critical angle, numerical aperture NA = √(n₁²−n₂²) and acceptance angle. Fibre optics carry virtually all of today's long-haul internet traffic, making these parameters central to modern telecommunications.
What is an optical fibre?
An optical fibre is a thin strand of glass or plastic with a high-refractive-index core surrounded by a lower-index cladding. Light injected into the core is trapped and guided along its length by total internal reflection, allowing signals to travel great distances with very little loss.
What is total internal reflection?
Total internal reflection happens when light travelling in the denser core meets the boundary with the less-dense cladding at an angle of incidence greater than the critical angle. Instead of refracting out, all of the light energy is reflected back into the core, so no mirrors are needed to confine the beam.
How is the critical angle calculated?
The critical angle is found from Snell's law as θc = arcsin(n₂/n₁), where n₁ is the core index and n₂ the cladding index. Because the ratio n₂/n₁ is just below one, the critical angle is large, so only steeply incident rays fail to undergo total internal reflection.
They set the refractive indices of the two glass regions. The simulation forces the core index n₁ to stay above the cladding index n₂, since guiding requires the core to be optically denser. Bringing the two values closer together shrinks the index difference, which narrows the acceptance cone and lets fewer rays be guided.
Numerical aperture (NA) measures the cone of angles over which a fibre can accept and guide light. It is calculated as NA = √(n₁²−n₂²), and the acceptance half-angle follows from θa = arcsin(NA). A larger index difference gives a higher NA and a wider acceptance cone.
A ray is guided only if its angle from the fibre axis stays within the acceptance angle, which is equivalent to its wall incidence exceeding the critical angle. Rays launched too steeply violate this condition, refract through the core wall and escape into the cladding. The simulation draws these escaping rays in red.
Single-mode fibre has a small core and a tiny index difference, so it supports just one guided light path and largely avoids modal dispersion, which is ideal for long-haul links. Multi-mode fibre has a larger core that supports many ray paths at once. The presets switch the simulation between these regimes.
The V-number, V = πdNA/λ, combines core diameter, numerical aperture and wavelength to indicate how many modes a fibre supports. When V is below about 2.405 the fibre is single-mode, carrying one mode; larger values allow many modes. It governs the trade-off between core size and bandwidth.
The critical angle, numerical aperture and acceptance angle are computed from the standard ray-optics formulae and update correctly with the sliders. The animated zig-zag rays are a simplified visual model rather than a full electromagnetic mode solver, so they illustrate the geometry of guiding faithfully without modelling wave effects such as interference.
Optical fibres carry the backbone of the global internet, linking data centres, cities and continents with terabit-per-second capacity. They are also used in medical endoscopes, fibre-optic sensors, and high-speed local networks. Their immunity to electromagnetic interference and very low signal loss make them superior to copper for long-distance communication.