• Pixel-art sticker of Fibrel, personifying Numerical Aperture of an Optical Fibre, with the caption “Catch The Light Inside My Cone.”

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Fibrel

Numerical Aperture of an Optical Fibre Physics

\[\text{NA} = \sqrt{n_1^2 - n_2^2}\]
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Meet Fibrel, a glass fibre who traps light that enters her end within a certain cone. Numerical aperture sets that cone: with core index 1.48 and cladding 1.46 it is about 0.24, accepting light within 14° of the axis. Charles Kao won the 2009 Nobel Prize. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
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Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

Meet Fibrel, a glass fibre who catches light that enters her end within a certain cone.

An optical fibre has a glass core surrounded by a cladding with a slightly lower refractive index. Light inside the core that hits the boundary at a shallow enough angle is totally reflected, and it zigzags along the fibre for kilometres.

Only light entering the end within a certain cone stays trapped. The numerical aperture measures that cone: NA = √(n₁² − n₂²), and the half-angle of the cone in air is θ = arcsin(NA). Light arriving more steeply leaks out through the cladding.

For a core with n₁ = 1.48 and cladding with n₂ = 1.46, NA ≈ 0.24, so the fibre accepts light within about 14° of its axis.

Charles Kao showed in 1966 that very pure glass could carry light over long distances, and he shared the 2009 Nobel Prize in Physics for it. Fibres now carry most of the internet's traffic under the oceans.

Equations

\[\text{NA} = \sqrt{n_1^2 - n_2^2}\]
SymbolMeaningUnit
\(\text{NA}\) numerical aperture \(\mathrm{dimensionless}\)
\(n_1\) core refractive index \(\mathrm{dimensionless}\)
\(n_2\) cladding refractive index \(\mathrm{dimensionless}\)

Sources

  1. OpenStax University Physics Vol. 3 — Total Internal Reflection
  2. NobelPrize.org — The Nobel Prize in Physics 2009
  3. Wikipedia — Numerical aperture

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