Critical angle and total internal reflectionEdexcel International A Level Physics: Revision notes

Total internal reflection (TIR) is the complete reflection of light at a boundary, with no light refracted out. It occurs only when both conditions are met:

• the light is travelling from a medium of higher refractive index towards one of lower refractive index, for example glass to air
• the angle of incidence is greater than the critical angle

TIR can never occur when light travels towards a medium of higher refractive index.

The critical angle C is the angle of incidence in the denser medium for which the angle of refraction is 90°, so the refracted ray travels along the boundary. Putting θ₂ = 90° in Snell's law gives n₁ sin C = n₂. For a boundary with air (n₂ = 1):

sin C = 1/n

The larger the refractive index, the smaller the critical angle. For a general boundary between two materials, sin C = n₂/n₁ with n₁ > n₂.

Worked example. Glass n = 1.52: sin C = 1/1.52 = 0.658, so C = 41°. Diamond n = 2.42: C = 24°.

For light travelling from a higher to a lower refractive index:

• angle of incidence < C: most light refracts away from the normal, with a weak partial reflection
• angle of incidence = C: the refracted ray emerges along the boundary at 90°
• angle of incidence > C: total internal reflection, and the angle of reflection equals the angle of incidence

To predict whether TIR occurs: work out C for the boundary, check that n decreases across it, then compare the angle of incidence with C.

TIR is used in optical fibres, where light signals are guided along a glass core by repeated total internal reflection at the core wall, with very little loss. It is also used in prisms in binoculars and periscopes, and in the sparkle of cut diamond: its high refractive index gives a small critical angle (24°), so a large fraction of the light inside is totally internally reflected and emerges from the front face.