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Total internal reflection is the complete reflection of light back into the material it came from. It occurs when light travels from a material with a higher refractive index into one with a lower refractive index and hits their boundary at an angle greater than the critical angle.
What total internal reflection means
When light reaches a boundary between two materials, it can reflect, refract (change direction as it enters the second material), or do both. Under the right conditions, no light propagates into the second material: the light reflects back into the first. That is total internal reflection (TIR). OpenStax explains the phenomenon, and the Optical Society’s guide to Snell’s law, reflection, and refraction describes the boundary behavior.
What conditions produce it?
Both conditions must be met:
- Light approaches the boundary from the material with the higher refractive index: n₁ > n₂.
- The incidence angle, θ₁, is greater than the critical angle, θc.
Angles are measured from the normal: an imaginary line perpendicular to the boundary at the point where the light strikes. Measuring from the surface instead would give a different angle and lead to an incorrect comparison with the critical angle.
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Snell’s law relates the refractive indices and angles on either side of the boundary: n₁ sin θ₁ = n₂ sin θ₂. At the critical angle, the refracted ray travels along the boundary, so θ₂ is 90°. Because sin 90° = 1, the critical angle is:
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θc = sin⁻¹(n₂/n₁), when n₁ > n₂.
For example, HyperPhysics gives 48.6° for a water–air boundary. That is a reference example, not a universal angle for every water–air setup; the result depends on the refractive indices used and the light conditions.
What happens below, at, and above the critical angle?
- Below θc: Some light refracts into the lower-index material and some reflects.
- At θc: The refracted ray runs along the boundary, at 90° to the normal.
- Above θc: In the elementary ray description, there is no propagating refracted ray; the light reflects back into the higher-index material.
Where total internal reflection is used
Optical fibers and waveguides guide light
A higher-index core surrounded by lower-index material can keep light traveling along a route through repeated internal reflections. Fiber optics carry communications signals, and image-forming fiber bundles are used in endoscopes. OpenStax describes fiber optics as a widely used application of TIR.
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Prisms redirect light in instruments
Reflective prisms can use TIR to turn light within an optical instrument. OpenStax discusses their use in binoculars and identifies periscopes as another application: College Physics 2e, section 25.4.
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TIR contributes to diamond sparkle
Diamond’s high refractive index makes total internal reflection relevant to its sparkle, but TIR is one contributor to the appearance, not a complete explanation of every optical effect involved.
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