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What is the critical angle for total internal reflection?

The critical angle is the minimum angle of incidence at which total internal reflection occurs when light travels from a medium with a higher refractive index to one with a lower refractive index.

When light hits the boundary between the two media at exactly the critical angle, the refracted ray travels along the boundary between the media. If the angle of incidence is greater than the critical angle, the light is completely reflected back into the denser medium—this is total internal reflection.

The critical angle depends on the refractive indices of the two materials:

  • It is smaller when the difference in refractive indices is greater.
  • For example, the critical angle for light going from glass (n ≈ 1.5) to air (n ≈ 1.0) is about 42°.
  • From water (n ≈ 1.33) to air, the critical angle is about 49°.

Total internal reflection can only occur if the light is traveling from a denser to a rarer medium, and the angle of incidence exceeds this critical angle.

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