Sci: Refraction

 In my youth, we scientific types routinely solved problems that involved a steel girder of negligible mass, suspended at its centre of gravity by a silken thread, and before we were too far advanced, we heard our first physics joke.

It was about the three scientists who were trying to pick the winner of Australia’s premier horse race, the Melbourne Cup, which is held each November. The first, a mathematician, gathered a wealth of data on weather, rainfall, wind, pollen counts and other possible influences, and three years in a row, failed dismally to pick a winner.

At the end of those three years, the geneticist had just finished drafting a plan for a breeding program that should, in five generations, produce a winner, but the physicist had got it right, three times in a row. The others asked the physicist how it was done. She reached into her pocket, pulled out an envelope and turned it over. Then she drew a circle on the back. “Consider,” she said, “a spherical horse running in a vacuum…”

Refraction and refractive index

If you don’t know what a sine is, you may prefer to skip this section.

This diagram shows a light ‘ray’ going from a less dense medium to a denser one, and the refractive index is given by x/y.

Whenever light passes through transparent materials, it slows down. The weird thing is that when the light passes out of that material, the speed changes back up again. We call this change refraction, and the speed change sets a measure called the refractive index.

Just trust me for now that this index is equal to the ratio of the speed of light in a vacuum to the speed of light in the material, and it can be measured in a number of ways. The classic measure is to map a single ‘ray’ of light as it passes into material, with the refractive index being the ratio of the sine of the angle of incidence to the sine of the angle of refraction. (Of course, there’s no such thing as a ‘light ray’, but because it makes thinking and calculation easier, we pretend that there is—remember the spherical horse?)

Every sort of wave can be bent, which is what refraction is all about. Light rays refract when they pass through a medium of different density, as when light travels from air into glass. When light passes into a region of increased density like this, it bends towards the normal, a line perpendicular to the surface where the light enters the other material. When light passes into a region of reduced density, it bends away from the normal.

Refraction happens to all forms of wave, even ocean waves, sound waves and earthquake vibrations, as well as light and radio waves, just so long as the waves are moving from a medium of one density to a different medium. In the case of sound, the dense damp air over calm water at night makes sound “travel over the water” by bending down the sound that would otherwise radiate upwards, while earthquake P waves can be significantly refracted as they pass through rock boundaries.

Estimating the refractive index of water

The apparent depth of water is reduced by refraction in the same way that light is bent. If you can get a deep glass container such as a large measuring cylinder, a fish tank or a long vase, and drop a coin into it, you will be able to estimate the refractive index of water.

Estimating the refractive index of water.

Set up the equipment like this, and then look down into the water while you move your hand down until you think your finger (outside the container) is level with the coin inside the container.

If you measure the real depth and the apparent depth, the refractive index is just the real depth divided by the apparent depth. You can see the effect, even with a water glass, but it’s harder to get an accurate measure. A deeper container gives a better estimate.

Out of sight

The coin is there in both glasses: why can’t we see it in the glass on the right?

Place a coin on a black piece of paper. Put a clear glass filled with water on top of the coin. Can you see the coin? Where is the best place to see it? Now look from the side. Can you see the coin without looking straight down through the water glass?

Why it is hard to spear fish

A safer spear that is easier to find in a kitchen.

When you put a pencil, a wooden spoon or some other straight object into a glass like this, you will see this sort of bending. Refraction must have been known from the very first time somebody tried to spear a fish in water, aiming at an angle. To see why this must be so, put a coin in a deep pan, cover it with five centimetres of water, and approaching at an angle of 45°.

Then try to poke the centre of the coin with a pencil. The result, every time, will be that you miss the ‘fish’, because it is not where you think it is. If you want to hit a fish, you have to have your spear partly in the water, and aim the part of the spear which is in the same medium as your target, a bit of physics known to every society that fishes with a spear from boats or the land.

In the interests of the fish, I won’t say any more, but it comes down to the problem that you are aiming a spear that is in the air at a fish that is in the water. Take it from there.

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