Bendy Light

How does adding sucralose (sugar) to water change how the light moves through it?

Light travels in a straight line. If it weren’t for this property of light there wouldn’t be shadows or laser pointers. This rule, however, isn’t completely true.

When light moves from one material to another it changes its path. Some of the light changes its direction by reflecting and some changes direction by refracting. When a light ray goes from one transparent or translucent material to another, it continues to move through the material but not in the same direction. This change in direction is called refraction.

In the year 984 Ibn Sahl noticed that light did this when it moved through a lens, and he wondered if there was a rule that said how much light changed direction. He found that as light moved from air to the glass of the lens that the amount it refracted depended on the angle at which the light hit as well as the type of glass he used. He realized that the light was also changing speed.

In 1621 both Willebrord Snellius and Renee Decartes both found an equation that tells how much of a light ray will reflect and how much will refract when the light hits a surface. Both of these depend on a number called the index of refraction, or “n”. The larger the index of refraction of a material, the more light it will reflect and the more it will bend the light that is transmitted. The index of refraction also tells how fast light travels in the new material. Light is fastest when it is moving in a vacuum. No, not a Hoover, in this case “moving in a vacuum” means that light is moving through nothing, no matter at all, not even air.

Outer space is an example of a vacuum. In a vacuum light travels at 300,000,000 meters per second but that’s as fast as it can go. If it travels in any type of matter, even air slows down a little bit. As it slows down, it changes directions. Because the index of refraction tells how fast light goes in a particular material, it can also say how much light changes direction as it moves from one material to another. It can also tell us how much light will be reflected.

The speed of light in a material is related to the index of refraction by the formula: n=c/v, where c is the speed of light in a vacuum and v is the speed of light in a material.

The index of refraction depends on many things. Mostly it depends on the type of material. Water has an index of refraction of 1.3 while diamond has an index of refraction of 2.4. This means that diamond reflects more light than water and that light goes 2.4 times slower in diamond than it does in a vacuum. Index of refraction can also depend on temperature. The index of refraction of cooler air is 1.0003, but when the air is heated by 100 degrees C it changes to 1.0002. This may not seem like much but it bends light enough to cause the wavy appearance seen on top of roads and the hood of your car on hot days.

When we look at an object through a transparent material, such as water, we can see that the light is bending because it looks like the object has shifted a bit. Try this with a glass of water and a pencil. See Fig. 1.

When you put the pencil in the water it looks like the part that is in the water is disjointed from the part that is still in air. This is because of refraction. But what happens when two different materials have the same index of refraction? Could we see them? We can see transparent materials because of the reflections and in some cases because objects seen through these materials seem distorted by refraction.

The index of refraction is different from that of air. But what would happen if two objects had the same index of refraction? Would we be able to distinguish between the two? Would one seem to disappear? That is what the students will be investigating with this experiment.

The gel cubes are grown in water and because the final cube is 99% water, it has the same index of refraction as water. While in water, it seems to disappear but in air it is clearly visible. Water with sucralose in it has a different index of refraction than plain water, and water with sugar has yet another index of refraction. When the gel cubes are grown in sugar water or sucralose water they end up with the same index of refraction as sugar water or sucralose water.

By shining a laser, which travels in a straight line unlike light from a flashlight, through the gel cubes and tracing the laser beam, the students are able to see exactly how much the light is bent by the cube. See Fig. 2.

When they do this for the three different cubes and then compare the results, they can see that the light changes direction more through some materials than others. If you would like to take this one step further, you could use a protractor to measure the angles involved to see exactly how much the light is bent for each case.

• Real world connections:
  • Find or bring in transparent objects the students use in their daily lives and have them create a index of refraction index for household objects.
  • Have students experiment with transparent → opaque objects to see how this changes the index of refraction.
• Suggestions for drawing, illustrating, presenting content in creative ways:
  • Have students use a typical prism photo and a protractor to measure the angle of refraction for each color of the spectrum and draw their own.
• Engineering and design challenges connected to the content. Example: Teach Engineering