Ideas

1. Lissajous Figures

Lissajous figures can be defined by a set of parametric equations which describes a complex harmonic motion. They can be seen several different ways such as through an oscilloscope or even using a laser shining on a spinning motor set up. One way of doing it is through this experiment.

2. Laser Problem

I found this problem after a discussion about billiard problems one friday in the lab. Project could show the mathematics behind the problem. Maybe even create a model of it or try to fit it for different shaped rooms.

3. Invisibilty with mirrors or optical cloaking

A series of mirrors and angles make this effect work. For this it would be possible to make a table top verison of it and use rate tracing to make diagrams of it. Seen demonstrated in this video and a smaller verison of the whole contraption can be seen here.

4. Measuring the instantaneous distance to the Moon

This experiment was found on the ajp website. It uses a telescope on a motor-driven mount and a digital camera then using some mathematics and angle sizes you can figure out the distance between your location and the Moon. Maybe it's possible to conduct without a telescope?

5. Anamorphic images

Anamoprhic images are images that appears normal when viewed from a specific perscpective or viewed through something that transforms the image like a mirror. This website has nice examples of different anamorphs. We could make our own anamorhpic image that is revealed by looking in a cylindrical mirror using mathematics shown in this link.

6. Pepper's Ghost

The ghosts you see on the Haunted Mansion ride at Disney are done using this effect. People are using it for various different purposes for example it has even been used in a runway show! This is a great website with various examples of Pepper's Ghost effect and has a nice video showing how the effect works. With this one could make their own set up of the effect to demonstrate it.

7. Demonstration with Hall of Mirrors

The Hall of Mirrors is a popular room in any funhouse. The set up of mirrors makes it very difficult to see were one is going or the proper way out. We could use this idea to make our own setup of it, determine where a laser would go through the maze or see if we could design a way so that the laser would get through the entire maze, or somehow connect it with billiard problems.

8. Billiard Problems

A nice definition of the billiard problems can be found here. This relates back to the laser problem mentioned above.

9. Metamaterials

Metamaterials are artifical materials engineered to exhibit properties that are not found in nature. They can be created to bend electromagnetic waves so that what we see is what is actually behind the material. So far science has only been able to make this work with microwaves and sonar. The subject is very complex and may not be suitable to do a project on because it does involve nanomaterials. It may be possible to make a larger scale model of what some of the metamaterials look like.