MAP PHYSICS LAB · OPTICS · MAP 22

How does light stay inside a fibre?

Follow a ray into the core, then inspect what happens at the core–cladding boundary. Explore refraction, the critical angle and the acceptance cone.

Explore the ray

Entry angle α

Measured from the fibre axis, outside the core.

Core refractive index

Cladding refractive index

Critical angle, θcAt the core–cladding boundary

Acceptance half-angle, αmaxAt entry from air

Numerical aperture

The ray through the fibre

Core and cladding are shown in a longitudinal section.

Incident / reflected pathRefracted pathReference lines

Try this:

Show explanation and equations

At any boundary: n₁ sin θ₁ = n₂ sin θ₂
Critical angle: sin θc = ncladding / ncore, when ncore > ncladding
At the fibre entrance: nair sin α = ncore sin θ
At the wall: i = 90° − θ
Numerical aperture: NA = √(ncore² − ncladding²) = nair sin αmax

The external acceptance angle αmax is not generally 90° − θc. That complementary angle is the maximum internal angle θ to the fibre axis.

Ideal, straight step-index fibre in air (nair = 1). Rays lie in a plane through the fibre axis. This ray model omits material attenuation, bending losses, diffraction and waveguide modes. Entrance and exit Fresnel losses are omitted in the fibre view; leakage at the first wall is shown. The single-boundary power fractions use Fresnel equations for unpolarised light at a lossless interface. Line brightness is illustrative. The trace dot shows the path, not light speed. At the critical angle, the dashed refracted direction is the limiting direction along the boundary, not a transmitted beam carrying power across it.