This topic accounts for approximately 9% of your exam marks.
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Ray diagrams, Snell's Law and critical angle calculations appear regularly.
When refraction stops working
As the angle of incidence inside a dense medium is gradually increased, the angle of refraction in the surrounding less-dense medium also increases, but it grows faster than i, because the ray is bending away from the normal as it leaves
Eventually, at one particular incident angle, the refracted ray bends right round to lie flat along the boundary (refraction angle = 90°). This incident angle is called the , c
Any incident angle larger than the critical angle can no longer produce a refracted ray at all; all the light is instead reflected back inside the dense medium
Definition
Total internal reflection (TIR) is the complete reflection of a wave back into its original medium when:
the ray is travelling from a denser medium into a less dense one (so refraction would bend it away from the normal), and
the angle of incidence is greater than the critical angle
Both conditions are needed; if the light is travelling from less dense to denser, no critical angle exists
Exam tip
Explaining or identifying total internal reflection
What comes up: "Explain why light does not pass through the boundary" or "State the conditions required for total internal reflection."
Write (three marks): (1) State that total internal reflection is occurring — all light reflects back into the denser medium instead of refracting through. (2) The light must be travelling from a medium with a higher refractive index into one with a lower refractive index (denser to less dense). (3) The angle of incidence inside the denser medium must exceed the critical angle for that boundary.
Watch out: Both conditions must be stated — denser-to-less-dense direction AND angle greater than the critical angle. Giving only one condition earns only one of the two condition marks.
Critical angle and refractive index
sin c = 1 / n
Rearranges to:
c = sin⁻¹(1 / n)
n = 1 / sin c
A consequence: the larger the refractive index, the smaller the critical angle, and the more easily light gets trapped by TIR. This is exactly why cut diamonds (n = 2.42) sparkle so brightly; most rays striking the diamond's back surfaces have angles bigger than the critical angle and bounce repeatedly inside the gem before emerging
Useful applications of TIR
Optical fibres:
A long, thin core of high-refractive-index glass (or plastic) is surrounded by a slightly lower-index outer cladding
Light injected at one end of the fibre keeps striking the core–cladding boundary at angles bigger than the critical angle, so it total-internal-reflects along the entire length, even round bends
Applications:
telecommunications: fibre-optic cables carry the world's internet traffic at near-light speed, using infrared pulses
medical endoscopes: a flexible bundle of fibres carries an image of the inside of a patient's body out through a small incision
decorative lighting: fibre lamps glow at the tip from a light source at the base
Right-angled prisms:
A right-angled prism cut from glass has a critical angle of about 42°; a ray striking its long face at 45° therefore undergoes TIR
Applications:
periscopes: a vertical tube with a right-angled prism at the top and another at the bottom turns light through 90° twice, letting a viewer below see what is above the obstruction
binoculars and telescopes: internal prisms fold the light path so the instrument can be made short and still have a long total path
bicycle and road safety reflectors: built from tiny corner-cube prisms that bounce headlight light straight back to the source
