By the end of this week I will be halfway through with the REU program. I have accomplished a lot of work on my website and have been delving far into all the different application of index of refraction. I took out two interesting books from the library, one titled: Rainbows, Halos, and Other Wonders by Kenneth Heuer. I realized that most of the effects that can be seen in the atmosphere deals with changes in an index of refraction. Some discussions on diffraction is also mentioned but things such as mirages deal with layers of varying indexes of refraction. I am currently working on a nice webpage with facts that I learned both from this book and from reading online websites. I also found a great website with some beautiful pictures of actualmirages. Most of these pictues were taken in Finland. There are certain parts of the world that are more common to mirages because of the climate factors necessary to induce them.

I also took out one other book title, Descarte's Natural Philosophy. In this book there is a whole title with Descarte's theories for index of refraction. It is a little difficult to read but there are some interesting scientific philosophies in there.

This week I also found some interesting ideas for refractometers to develop that I can use for making measurements of my sugar solution tank which is still residing in the lab helping to house the homeless mold.

In general, I have learned that one of the easier ways to measure the index of refraction would be to try to find the critical angle when passing from something such as glass to the sugar solution. In order to measure a critical angle you have to pass from a higher index of refraction to a lower index of refraction. This can be difficult with a fish tank however because a laser pointer will be passing from air to glass which is from a lower index to a higher index. This will refract the laser pointer from reaching the critical angle at the sugar solution. A more indirect method needs to be devleloped.

However once the critical anlge is determined it is very simple to solve for the index of refraction of the second material. With measuring the critical angle and taking into account the fact that the refracted ray is 90 degrees, and the knowledge of one of the indexes of refraction, it is simple geometry then to determine how much the index of refraction will vary in a tank filled with sugar water for a few weeks. In trying to manipulate the direction of the laser pointer it is important to take into account that the ray entering a higher index will bend towards the normal. When it enters a medium having a lower index, the ray will bend away from the normal.

There were some ideas developed that could manipulate the laser pointer to totally internally reflect. Demonstrating total internal reflection with the laser pointer in the fish tank would be a great visual demonstration that I can show at my presentation. So this is an idea that I plan to fully develop.

One idea was to lower a tube with an angled edge. When the laser pointer is directed down to it, this can determine the critical angle becuase then it will be total internally reflected off this glass where the boundary is higher than that of the solution. Since the laser beam is going to be shone directly downward it will not refract with the air. The test tube is designed to be angled because that way the laser can always meet the air perpendicularly while it will have to be refracted off the glass.

A second idea was an interesting one and my favorite. It is interesting because of the way that it will manipulate the laser to total internal reflection. It does this thro a semicircular test tube lowered into the tank. This allows the laser pointer to hit the interface of the fish tank perpendicularly and then the test tube can be rotated and the flat edge on the other side will be angle to the laser pointer according to a critical angle.