Every time you stream a video, the data almost certainly spent part of its journey as flashes of light inside glass fibres thinner than a hair, running under streets and across ocean floors. The light stays trapped inside the fibre even around bends, without any mirror coating. The trick is a special case of refraction called total internal reflection, and it only needs two conditions.
When light goes from a larger index to a smaller index (glass to air, water to air) it bends away from the normal, so (for any angle other than ) the refracted angle is bigger than the incident angle. As the angle of incidence increases, the refracted ray swings closer and closer to the surface. At one particular angle, called the critical angle , the refracted ray travels exactly along the surface, at to the normal. Beyond that angle there is no refracted ray at all: all of the light reflects back into the first medium.
Two conditions for total internal reflection
1) The light must be travelling from a medium with a larger index of refraction into one with a smaller index (for example glass to air). 2) The angle of incidence must be greater than the critical angle. If either condition fails, at least some light refracts out.
| Boundary | Critical angle |
|---|---|
| Water () to air | |
| Glass () to air | |
| Crown glass () to air | |
| Diamond () to air | |
| Glass () to water () |
Total internal reflection at work
- Fibre optics: a glass core is wrapped in cladding with a lower index. Light hits the core-cladding boundary at more than the critical angle and reflects all the way along, even around gentle bends. Fibres carry internet and phone signals and, in a medical endoscope, let a doctor see inside the body.
- Diamonds: with a critical angle of only , light that enters a well-cut diamond reflects many times inside before escaping through the top facets, which makes it sparkle. Dispersion spreads the escaping light into flashes of colour.
- Prisms in binoculars and periscopes: light meets the inside face of a glass prism at , more than glass's critical angle, so it is totally reflected. A prism reflects nearly 100% of the light and never tarnishes, so it beats a silvered mirror.
A Nobel Prize for light in glass
The 2009 Nobel Prize in Physics was shared by Charles Kao, for showing how to send light through glass fibres over long distances, and by Willard Boyle and George Smith for the CCD image sensor. Boyle was born in Amherst, Nova Scotia. Fibre-optic technicians who install and splice these cables are in demand across Canada.
Refraction in nature
- Apparent depth: light from an underwater object bends away from the normal as it leaves the water, and your brain traces it back in a straight line to a point that is too shallow. Looking nearly straight down, for water: a pool looks only deep.
- Mirages: on a hot day, air right above a road is hotter and has a slightly lower index than the cooler air above. Light from the sky heading down at a shallow angle is bent more and more away from the normal until it curves back upward into your eye (a total internal reflection that happens gradually). You see an image of the sky on the road, which looks like water.
- Shimmering (heat haze): pockets of warm and cool air with slightly different indices drift and mix, so the path of light through them keeps changing and objects behind them waver. Stars twinkle for the same reason.
- Rainbows: sunlight enters a raindrop and refracts, splitting into colours (dispersion); it reflects off the back inside surface of the drop (a partial reflection, not a total one: most of the light passes out the back) and refracts again on the way out. Red light leaves at about from the direction opposite the Sun and violet at about , so you see a rainbow only with the Sun behind you.
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