Episode 318: Total internal reflection

Total internal reflection (TIR) is a consequence of refraction.


  • Student experiment: Ray tracing using semicircular block (30 minutes)
  • Discussion: Uses of TIR (15 minutes)
  • Demonstration: Transmitting a radio programme using fibre optic cable (10 minutes)
  • Worked example: Critical angle (10 minutes)
  • Student questions: On TIR (30 minutes)

Student experiment: Ray tracing using semicircular block
Students can shine rays of light into the curved face of a semicircular glass or perspex block.

Total internal reflection

Ask students to mark the centre of the straight edge with a fine permanent pen before they start. There are a few qualitative questions and answers included.

Emphasise that total internal reflection can only happen when the light goes from high to low refractive index (from the ‘denser’ to the ‘less dense’ medium). It will show on their calculators as an error message if the refracted angle would be greater than 90o. The critical angle is always in the denser medium.

Episode 318-1: Ray tracing on the way out (Word, 44 KB)

Discussion: Uses of TIR
Consider some of the uses of TIR. Prisms are used in cameras and binoculars. A 90° prism can be used to turn light through 90° (reflects at the hypotenuse) or 180° (in through the hypotenuse and reflects off both short sides). If critical angle for the prism material is about 42° then it is totally internally reflected because the angle of incidence will be 45°from geometry. The reflection is more efficient than with a silvered mirror.

Optical fibres are the most important use nowadays. A simple fibre or glass rod will lead the light along because the air outside is less dense than the glass. The shape ensures that the angle of incidence is greater than critical, around 42o. The addition of cladding improves the efficiency. In order to confine the light to paths almost straight down the centre and reduce time differences due to different paths or wavelengths, it is best to have the critical angle large, e.g. over 80o. This is achieved by the cladding. Usually for transmission of signals a monochromatic semiconductor laser is used.

Episode 318-2: Fibre optics (Word, 77 KB)

Demonstration: Transmitting a radio programme using fibre optic cable
Show data transfer on an optical fibre. This can be very quick if it is set up before hand.

It is convincing to see the light in the pipe and hear the broadcast start as it is inserted into the transmitter or receiver.

Episode 318-3: Data transfer on an optical fibre (Word, 43 KB)

Worked example: Critical angle
Calculate the critical angle in water at an air boundary.

The critical angle in a medium is related to the refractive index of the medium by

n = 1/ sin C or sin C = 1/n

so sin C = 1/1.33 = 0.752 and C = 48.8°

Student questions: On TIR
Some practice questions on total internal reflection

Episode 318-4: Questions involving total internal reflection (Word, 27 KB)

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Episode 318: Total internal reflection  (Word, 152 KB)