Optical fiber uses reflection to guide light through a channel, in which angle…

CONCEPT

Total internal reflection occurs when light travels from a medium of higher refractive index toward one of lower refractive index and its incidence angle exceeds the critical angle. At the critical angle, the refracted ray is tangent to the boundary; below it, refraction into the second medium occurs.

For a core–cladding interface, the critical-angle relation is sin θc = ncladding/ncore, with ncore > ncladding.

APPLICATION

In an optical fiber, light meets the core–cladding boundary from the higher-index core. Guiding by repeated internal reflection therefore requires the incidence angle at that boundary to be greater than the critical angle.

CONTRAST

• Equal to: the refracted ray travels along the interface, marking the limiting case rather than total internal reflection.

• Less than: part of the light refracts into the cladding, so the ray is not confined by reflection.

• Greater than: the ray undergoes total internal reflection at the core–cladding boundary.

• Less than or equal to: this range includes refraction below the limit and the tangent-ray boundary case.

CROSS-CHECK

For ncore = 1.50 and ncladding = 1.40, sin θc = 1.40/1.50, so θc ≈ 69.0°. An incidence angle above 69.0° produces total internal reflection, confirming the relation greater than.