Fiber Optics
Trapping light inside a thread of glass
This concept builds on Snell's Law — Mapping the Angle of Refraction. Consider exploring it first for the best experience.
Light Bends as It Enters the Glass
The red laser on the left shines into the flat end of a glass fiber. Glass slows light down, so the beam bends toward the dashed axis as it crosses into the core: Snell’s law gives sin(launch angle) = n₁ · sin(inside angle). Move the "Launch angle" slider and compare the two angles printed at the top left of the canvas.
Trapped by Total Internal Reflection
Inside, the beam reaches the core wall. Beyond it lies the cladding, a glass with a slightly lower index n₂. If the beam meets the wall at more than the critical angle, where sin(critical angle) = n₂ / n₁, no light can cross: all of it reflects. The green arc at the first wall hit shows that angle beside the critical one.
The Acceptance Cone
A steeper launch makes a steeper zig-zag, so the beam meets each wall at a smaller angle. Past the edge of the green acceptance cone, that angle drops below critical and every bounce leaks some light, drawn as gold rays escaping through the cladding. Move the "Launch angle" slider across the cone edge and watch the detector bar and the "Light delivered" readout.
Why the Cladding Matters
The cladding protects the guiding surface, and its index sets the cone. Move the "Cladding index n₂" slider toward the core index: the critical angle grows and the cone narrows. Set n₂ equal to n₁ and the cone vanishes, so light simply passes out of the core. Raising the "Core index n₁" slider widens the cone again.
Worked Example: Glass Core, Glass Cladding
Take n₁ = 1.50 and n₂ = 1.40. The critical angle is sin⁻¹(1.40 / 1.50) = 69.0°. The numerical aperture is √(1.50² − 1.40²) = √0.29 = 0.54, so the acceptance cone is sin⁻¹(0.54) = 32.6°. Launched at 20°, the beam travels at 13.2° inside and meets the wall at 76.8°, above 69.0°, so it is trapped. Launched at 40°, it meets the wall at 64.6° and leaks.
Bends Leak Light
Move the "Bend" slider to lift the fiber over a hump. Where the fiber curves, its outer wall tilts toward the oncoming beam, so the angle at that wall drops. Gentle bends change nothing, but past a few core widths of radius the angle falls below critical and light escapes. Rays launched near the edge of the cone are the first to go.
Many Paths, Different Arrival Times
Press "Ray fan" to send five rays at once, from straight along the axis up to your launch angle. The steeper rays zig-zag further, so their pulses arrive later. At 20° the steepest path is 2.7% longer: in 1 km of this fiber the straight pulse takes 5.0 µs and the steep one about 0.14 µs more. That spreading blurs fast signals together.
How It Works — Step by Step
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1
Light Bends as It Enters the Glass
The red laser on the left shines into the flat end of a glass fiber. Glass slows light down, so the beam bends toward the dashed axis as it crosses into the core: Snell’s law gives sin(launch angle) = n₁ · sin(inside angle). Move the "Launch angle" slider and compare the two angles printed at the top left of the canvas.
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2
Trapped by Total Internal Reflection
Inside, the beam reaches the core wall. Beyond it lies the cladding, a glass with a slightly lower index n₂. If the beam meets the wall at more than the critical angle, where sin(critical angle) = n₂ / n₁, no light can cross: all of it reflects. The green arc at the first wall hit shows that angle beside the critical one.
-
3
The Acceptance Cone
A steeper launch makes a steeper zig-zag, so the beam meets each wall at a smaller angle. Past the edge of the green acceptance cone, that angle drops below critical and every bounce leaks some light, drawn as gold rays escaping through the cladding. Move the "Launch angle" slider across the cone edge and watch the detector bar and the "Light delivered" readout.
-
4
Why the Cladding Matters
The cladding protects the guiding surface, and its index sets the cone. Move the "Cladding index n₂" slider toward the core index: the critical angle grows and the cone narrows. Set n₂ equal to n₁ and the cone vanishes, so light simply passes out of the core. Raising the "Core index n₁" slider widens the cone again.
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5
Worked Example: Glass Core, Glass Cladding
Take n₁ = 1.50 and n₂ = 1.40. The critical angle is sin⁻¹(1.40 / 1.50) = 69.0°. The numerical aperture is √(1.50² − 1.40²) = √0.29 = 0.54, so the acceptance cone is sin⁻¹(0.54) = 32.6°. Launched at 20°, the beam travels at 13.2° inside and meets the wall at 76.8°, above 69.0°, so it is trapped. Launched at 40°, it meets the wall at 64.6° and leaks.
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6
Bends Leak Light
Move the "Bend" slider to lift the fiber over a hump. Where the fiber curves, its outer wall tilts toward the oncoming beam, so the angle at that wall drops. Gentle bends change nothing, but past a few core widths of radius the angle falls below critical and light escapes. Rays launched near the edge of the cone are the first to go.
-
7
Many Paths, Different Arrival Times
Press "Ray fan" to send five rays at once, from straight along the axis up to your launch angle. The steeper rays zig-zag further, so their pulses arrive later. At 20° the steepest path is 2.7% longer: in 1 km of this fiber the straight pulse takes 5.0 µs and the steep one about 0.14 µs more. That spreading blurs fast signals together.
Key Takeaways
Total internal reflection guides the light
Light going from a higher index n₁ toward a lower index n₂ is completely reflected when it meets the boundary beyond the critical angle, sin θc = n₂ / n₁.
Only light inside the acceptance cone is trapped
Launching from air, the fiber accepts rays up to sin⁻¹(NA), with numerical aperture NA = √(n₁² − n₂²). A bigger index gap gives a wider cone.
Tight bends leak light
A bend tilts the outer wall toward the beam, lowering the angle of incidence below critical so some light escapes through the cladding.
Different paths spread a pulse
Steep rays travel further than straight ones, so a short pulse stretches out along the fiber. This limits how quickly pulses can follow each other.
Connected Concepts
Snell's Law
Every turn the light makes in the fiber — into the end face and at each wall — is Snell’s law at work.
Refraction
Light slows down in glass and bends at a boundary; total internal reflection is what happens when it cannot bend out at all.
Laser
A laser’s narrow, single-colour beam fits easily inside a fiber’s acceptance cone, which is why the two are used together.
Computer Networking
Most long-distance internet traffic travels as pulses of light through fibers like this one.
Electromagnetic Spectrum
Telecom fibers carry infrared light, just beyond the red end of what our eyes can see, where glass absorbs the least.