Reflection & Refraction
Waves · 1 question type
Exam Frequency Analysis
Past paper frequency (2018 to 2024)
This topic accounts for approximately 9% of your exam marks.
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
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
