Total Internal Reflection and Optical Fibres
When light tries to leave a dense medium at a steep enough angle, none of it escapes — it is all reflected back inside. That effect carries every phone call and internet packet through an optical fibre.
1. Building up to it
Consider light travelling from glass into air — from a denser to a less dense medium. It bends away from the normal, so the angle of refraction is larger than the angle of incidence.
As you increase the angle of incidence:
- Small angle: most light refracts out, a little reflects internally
- Larger angle: the refracted ray bends further, closer to the boundary
- At the critical angle: the refracted ray travels along the boundary — the angle of refraction is exactly 90°
- Beyond the critical angle: no light escapes — it is all reflected back inside
2. The critical angle
The critical angle (c) is the angle of incidence in the DENSER medium for which the angle of refraction is 90°.
sin c = 1 / n
Example: glass with n = 1.5.
- sin c = 1/1.5 = 0.667
- c = 41.8°
Example: water with n = 1.33.
- sin c = 1/1.33 = 0.752
- c = 48.8°
A LARGER refractive index gives a SMALLER critical angle — so light is trapped more easily in denser materials. Diamond (n = 2.42) has c ≈ 24.4°, which is why it sparkles: light entering it is internally reflected many times before escaping.
Finding n from c: rearrange to n = 1 / sin c.
Make sure your calculator is in DEGREE mode, and use sin⁻¹ to get the angle from the sine.
3. The two conditions
Total internal reflection occurs when BOTH of these are true: 1. Light travels from a DENSER to a LESS DENSE medium (e.g. glass → air) 2. The angle of incidence is GREATER than the critical angle
Both conditions must be stated for full marks. Giving only one — usually only the angle condition — was the recorded shortfall. Uncertainty about the conditions for TIR was recorded more than once.
It cannot happen going from less dense to denser. Light entering glass from air can never be totally internally reflected at that boundary.
The name explains itself: total (all the light, none refracted), internal (it stays inside the denser medium), reflection (it obeys i = r).
4. Optical fibres
An optical fibre is a thin, flexible glass or plastic strand that carries light by repeated total internal reflection.
Structure: a core of higher refractive index surrounded by cladding of lower refractive index. Light hits the core–cladding boundary at an angle greater than the critical angle, so it is totally internally reflected and bounces along the fibre — even around bends.
The cladding must have a LOWER refractive index than the core, so that the core is the “denser” medium and condition 1 is met.
Uses:
| Application | Why fibres are used |
|---|---|
| Communications (broadband, telephone) | huge data capacity, fast, low signal loss, immune to electrical interference |
| Endoscopes (medical) | look inside the body without surgery, using flexible fibre bundles |
| Decorative lighting, sensors | flexibility and light delivery |
The endoscope uses two bundles: one to carry light in to illuminate, one to carry the image out.
5. Prisms
A 45°–45°–90° glass prism turns light through 90° or 180° by total internal reflection. Since glass’s critical angle (~42°) is less than 45°, light striking the internal face at 45° is totally internally reflected.
Used in: periscopes, binoculars, and bicycle reflectors (which use TIR to send light straight back towards its source).
Prisms are better than mirrors here because they reflect 100% of the light — no metal coating to tarnish, and no faint secondary images from the glass surface of a mirror.
6. Other examples
- A swimming pool’s surface looks silvery from underwater at shallow viewing angles — TIR
- Mirages — light from the sky is refracted and totally internally reflected by hot air layers near the ground
- Diamonds sparkle because of their very small critical angle
7. Mistakes that cost marks
Giving only one of the two conditions.
Saying TIR happens from less dense to denser.
Using n = sin c instead of sin c = 1/n.
Forgetting sin⁻¹ when finding the angle.
Calculator in radian mode.
Saying the cladding has a higher refractive index.
Confusing the critical angle with the angle of refraction.
Saying some light still escapes beyond the critical angle — none does.
Frequently asked questions
What is total internal reflection? When light hitting a boundary from the denser side at an angle greater than the critical angle is entirely reflected back, with none refracted out.
What are the two conditions? Denser to less dense, and angle of incidence greater than the critical angle.
What is the critical angle? The angle of incidence in the denser medium giving an angle of refraction of 90°.
What is the formula? sin c = 1/n.
What is the critical angle for glass? About 42° for n = 1.5.
Does a bigger refractive index mean a bigger critical angle? No — a smaller one.
How does an optical fibre work? Light is repeatedly totally internally reflected at the core–cladding boundary.
Why does the cladding have a lower refractive index? So the core is the denser medium, allowing TIR at the boundary.
Why use prisms instead of mirrors? They reflect 100% of the light, with no tarnishing or secondary images.
Why do diamonds sparkle? Their very small critical angle traps light, which reflects internally many times.
Quick revision checklist
- I can describe what happens as the angle of incidence increases
- I can define the critical angle
- I can use sin c = 1/n in both directions
- I know a larger n gives a smaller critical angle
- I can state both conditions for TIR
- I know TIR cannot occur going into a denser medium
- I can explain how an optical fibre works
- I know the cladding has a lower refractive index
- I can give uses of optical fibres and their advantages
- I can explain the endoscope’s two bundles
- I can explain prism reflectors and why they beat mirrors
- My calculator is in degree mode
These notes cover total internal reflection and optical fibres in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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