Fibre optics numerical aperture
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Acceptance angle of a fibre.
NA = √(n₁²−n₂²)NA = √(n₁² − n₂²) = sinθ_max for the acceptance cone. Light entering inside the cone is trapped by TIR.
n₁ = 1.48, n₂ = 1.46: NA = 0.24, θ = 14°.
Larger NA collects more light but increases modal dispersion.
In more detail
The numerical aperture, NA = n sin θ, describes the light-gathering ability of an optical fibre or lens. It determines the acceptance angle for light entering the fibre.
Real-world uses
- Fibre optic systems are specified by numerical aperture.
- Microscope objectives are rated by numerical aperture.
- Engineers choose the numerical aperture of optical fibres to match the light source and the required coupling.
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Frequently asked questions
What is the acceptance angle?
The maximum angle at which light entering the fibre is guided by total internal reflection.
Why does NA matter for microscopes?
Higher NA gives better resolution and light collection.
What does numerical aperture tell me?
It shows the maximum angle at which light can enter the fibre and still be guided by total internal reflection.
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