Certain materials, such as glass and water, allow light to pass through it, but slower than it would in air or vacuum. The amount that is slowed down in a material is called the index of refraction (IOR).
This slowing down causes light to bend, or refract, at the surface of the material. The angles for refraction can be calculated with Snell's Law.
Snell's Law
n1 and n2 are the indices of refraction for the two materials. θi is the angle of incidence, and θr is the angle of refraction. (see diagram)
n1sin(θi) = n2sin(θr)
Additionally, a small amount of light is also reflected. This is called partial reflection, and it's strength is determined by the Fresnel equations. They are rather complicated, so just know that there is more partial reflection when light hits a material with a high IOR at a shallow angle. This is why when you look straight down at the ocean, it appears clear, but from a shallow angle, it appears reflective.
Snell's law does not always give an answer.* For example, when light starts in a material with a higher IOR than its surroundings, and hits the surface at a shallow enough angle, Snell's law provides no answer. When that happens, all of the light is reflected, which is called total internal reflection.
We'll look into each of these phenomena separately below.
| Some Common Indices of Refraction | |
| Material | IOR |
| Vacuum | 1 |
| Air | 1.0003 |
| Water | 1.333 |
| Glass | ~1.5 |
| Diamond | 2.4 |
Compared to mirrors, refractive materials, like glass, behave the opposite way. While concave mirrors focus light, concave glass spreads the light rays out. And while convex mirrors spread light out, convex glass focuses light.
You can even see how the mirrors would have behaved with the partial reflection of the glass.
The slider on the left controls how many times the light rays are allowed to "bounce," which includes both reflections and refractions.
To the right is a lens made out of two arcs of a circle. A horizontal beam entering this lens gets refracted at each surface, and focused onto a point. You'll notice that if the beam doesn't hit the center of the lens, it is not focused very well. This is called spherical aberration. Unfortunately, the parabola cannot save us from this aberration like it did with mirrors. When spherical aberration needs to be eliminated, people will often turn to a more complicated lens, like a Fresnel lens
By changing the thickness, height, and IOR of the lens, you can change where the focal point is. If you then take the cone lamp, and place it at the focal point, it will be focused into a horizontal beam. This is how the lens in a laser point creates a tight beam.
This also shows a magnifying glass can be used to light things on fire. Simply focus the light from the sun onto the surface of the object, and it will absorb the light as heat and catch fire.
To the right is a very simplified model of a moon (below), and a planet like Earth (above). The atmosphere has a slightly higher refractive index than the vacuum around it. This causes it to bend the light that hits the atmosphere but misses the planet. In reality, this refractive index would not be constant, but would vary with the altitude above the planet.
This refraction causes two phenomena. First, you can see the sun before it is rises. This is because some of the light rays coming from the sun get bent around the planet, and hit your eyes before the sun is really there.
The other phenomena is the shape of Earth's shadow. For most objects, like the moon, their shadows get larger the farther away from them you go. But by bending the light, the darkest part of Earth's shadow (the umbra) actually gets smaller. The area where the bent light travels, instead of being a full shadow, is now only a partial shadow (the penumbra).
All glass is one way glass, to some degree. In order to have one way glass, you just need one side to be very bright, and the other very dark. On the bright side, the partial reflection from the bright light will outshine any light transmitted through the glass from the dark side, making that side look like a mirror. On the dark side, the bright light transmitted through the glass will outshine the partial reflection from the dark light. You can try this to the right, and see that the brighter light tends to be more visible on both sides of the glass.
For actual one way glass, like in interrogation rooms, they often boost the partial reflection of the glass by either coating it with a thin layer of metal, or encasing the metal inside the glass (as shown to the right). This metal is so thin that it's translucent, but still quite reflective, which helps to reflect the light from the bright side.
Of course, if you're ever stuck in an interrogation room, and need to see through the one way glass, you could try to put your eyes right up on the glass, and cup your hands around them for a bit of shade.
One nice aspect of total internal reflection is the word total. Unlike mirrors, which absorb a bit of light with every reflection, no light is absorbed in total internal reflection.
To the right are two potential designs for cables that can carry light, much like how wires can carry electricity. You could use these cables to send information quickly over long distances. On the right is one made of mirrors, and on the left is one of glass. The mirror cable has a bit higher of absorption than normal, just to show what would happen over long distances.
As you can see, the cable made of mirrors will start to absorb so much light that barely any makes it through. The glass cable, on the other hand, lets the light through at full strength, though it can lose some around sharp bends.
The glass cable, because it loses so little light,* is the preferred one for communication uses. These kinds of glass cables are called fiber optic cables, and they are used to connect large portions of the internet.* This very website could easily have arrived on your computer via a fiber optic cable.
Well, that's all for refraction. Now you can try playing around with the light rays in this setup to the right.
Once you're done, you can move onto color.