I am doing a science fair project in which i want to see how the size of a pinhole effects the light diameter, and i would like to also relate this to focus and focal point. How would i do this?

Well, since it's a science project, it'd be a good idea to:

1. Learn about the theory involved, and depending on your math skills maybe calculate the pinhole size that you'd need for a reasonably focussed image.

2. Do an experiment! There are plenty of instructions on the web for creating a pinhole that works with a DSLR. If you have access to a DSLR, consider making pinhole lenses with holes of various diameter and compare the images that you get from each.

If the pinhole size that produces the best image matches the size you calculated, that'd be a great confirmation that your calculation was correct. If it doesn't, that might be even better -- you'd then have an opportunity to look at your calculation and try to figure out where you went wrong. Once you think you've found the problem, see if you can devise another experiment to confirm your hypothesis.

This kind of iterative approach, where you keep trying to refine your understanding and check your work with experiments is what science is all about. If you can use science to learn something, and if you present your findings clearly, you're going to be way ahead of the competition. And whether you win or not, in the end you'll have learned quite a bit.

I think this is a great project, actually. It seems simple, but there are a lot of important details. Intuitively, it seems obvious that the smaller the hole, the sharper the resulting image. But that might not really be true -- there might be such a thing as a pinhole that's too small. Either way, a very tiny hole may be problematic for other reasons, like exposure time. Beyond all that, just learning to make a good pinhole will be rewarding. What materials will you use? How will you make the hole? How can you improve the process? Can you make a pinhole that's similar in quality to a commercially produced pinhole? What happens if you change the distance from the pinhole to the sensor? You can take this project in lots of different directions. Have fun!