Critical angle
Intermediate
Angle beyond which total internal reflection occurs.
sinθ_c = n₂/n₁When light goes from a denser to a rarer medium, the refracted ray bends away; at the critical angle θ_c = sin⁻¹(n₂/n₁) it travels along the boundary. Beyond it there's total internal reflection.
Glass to air: 41.8°; water to air: 48.8°.
Needs n₁ > n₂.
In more detail
The critical angle is the angle of incidence in a denser medium above which total internal reflection occurs. It is given by sin θc = n2/n1.
Real-world uses
- Optical fibres are designed with angles above the critical angle.
- Diamonds sparkle because of their small critical angle.
- Engineers designing optical fibres use the critical angle to keep light trapped inside the core.
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Frequently asked questions
What is the critical angle for glass to air?
About 42 degrees for typical crown glass.
Does it apply from less dense to denser media?
No, total internal reflection only occurs going from denser to less dense media.
What happens beyond the critical angle?
Light is totally reflected at the boundary instead of refracting out, which is the basis of total internal reflection.
Related topics in Optics
Refractive index · Snell's law · Apparent depth · Total internal reflection · Applications of TIR · Prism and deviation