Total Internal Reflection

Total internal reflection (TIR) definition

When all light is reflected inside a medium instead of refracting out

Conditions for TIR

Light must travel from denser → less dense medium AND angle of incidence > critical angle

Critical angle definition

Angle of incidence that produces a 90° refracted ray

Critical angle formula

sin(c) = 1 ÷ n

n meaning

Refractive index of the denser medium

If i < critical angle

Light refracts out of the medium

If i = critical angle

Refracted ray travels along the boundary

If i > critical angle

Total internal reflection occurs

Reason for TIR

Light speeds up when leaving dense medium, bending away from normal

Optical fibres use

TIR keeps light trapped inside fibre for communication

Endoscopes use

TIR allows light to travel through fibre bundles inside the body

Prisms use

TIR used in periscopes, binoculars, cameras

Advantage of TIR

No energy loss; reflection is 100% efficient

Glass to air example

Common situation where TIR occurs

Water to air example

TIR can occur when looking up from underwater

Refracted ray behaviour

Only appears when i ≤ critical angle

Key idea

TIR happens only when angle is large enough and medium change is dense → less dense

The angles of refraction, critical and total internal reflection DIAGRAM