C11.9 Total internal reflection

• Light inside a high refractive index medium reaches a boundary with lower refractive index medium at angle to normal greater than critical angle. Ray of light completely reflected from boundary back into first medium - no energy refracted out. Critical angle depends on medium.

• Critical angle: the angle of incidence at boundary between 2 media which produces an angle of refraction 90degrees.
  - We can calculate from Snell’s Law when θ2 = 90degrees
  - If media 2 is air, n2=1, therefore n1sinC = 1, sinC = 1/n
  - n1sinθ1 = n2sinθ2 (light ray leaving). When θ2 = 90degrees, sinθ2=1, so n1sinθ1=n2, which means θ1is the maximum angle of refraction.
  - θ1 = C (critical angle)
  - For a light in a medium with refractive index n meeting an air boundary, sinC=1/n
  - For different boundaries, equation will be different
  - The greater the refractive index, the smaller the C

• Measuring refractive index:
  - Ray enters semi-circular block at 90degrees to curved boundary so direction doesn’t change.
  - Angle to the normal at flat edge is changed till TIR occurs
  - Critical angle C is measured and thus calculate n.

• TIR uses - optical fibres
  - Typically has inner core glass )n=2) and cladding glass layer outside (n=1.5)
  - Light in core undergoes TIR at boundary with cladding
  - It is NOT a hollow pipe

• TIR can happen anywhere waves meet boundary with medium where they travel more quicky.
  - E.g. sounds waves in water meeting the side of metal boat (sound travels faster in metal)

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