MathJax

28 March 2013

Optics and the Caveman Brain

You see with a Cave Man Brain



Ray-tracing in optics is one of those skills that is enjoyable to teach in class. A simple procedure, but with powerful results. Every year, I see a couple of students who struggled with the algebra of motion analysis who get a sense of accomplishment when mastering this technique. However, a few years ago, I noticed that many students seem to believe that the rays stopped at the image location. That is when I introduced the Giant Eye and the Caveman Brain.




I now start optics with a simple description of how the eye-brain combination works, that our brain has evolved to instinctively know that light has traveled a straight-line path from object to our eye. To illustrate, I get two volunteers to play a caveman and a fuzzy bunny.















We discuss the role of sunlight in seeing, how light reflects off the fuzzy bunny and goes in a straight line to the eye of the caveman. What would happen if the caveman's brain told the caveman that, while the light from the fuzzy bunny came from in front of him, the fuzzy bunny is over to the right? I have the caveman then throw a "spear" over to the right. I ask the class if this caveman will get to eat tonight. What if the brain told the caveman that the bunny was in the same direction that the light came from? The class caveman then throws the "spear" and "kills" the fuzzy bunny (a chance for some hammy acting). Caveman gets to eat tonight! And since I was on a roll, a couple of years ago, I added "Caveman makes fuzzy bunny slippers. Caveman gives to to cavewoman. (slight pause) Caveman pass on genes!"

While the actors are getting back to their seats, I emphasize that evolutionary pressure has made it so that we instinctively know that the light that enters our eye has traveled a straight line from object to eye. That lesson seems to help students understand lens and mirror optics later.

14 March 2013

If spring starts Thursday, why does Tuesday have 12 hours of daylight?

17 Mar has 12 hours of daylight, but spring is 3 days after. Why?

Why is the Vernal Equinox confusing to students of Latin.


Ask most people what happens on the first day of spring and you will get "12 hours of daylight and night" (i.e. equinox), which is close but not quite right. Some might say the northern hemisphere of the Earth is neither tilted away or toward the Sun. A few might even state that on that day, the equatorial plane of the Earth crosses the center of the Sun. However, these last two explanations, while correct, don't explain why the first day of 12 hour-daylight happens a few days earlier.

sunrise earth

The way I use in class to explain what is going on is to say that on the day of the vernal (or the autumnal) equinox is when it takes 12 hours for the center of the Sun to cross the horizon in the morning to when the center crosses the horizon in the evening. Since we start counting daylight when the first part of the Sun peeks above the horizon to when the last part of the Sun goes below the horizon, it becomes obvious that the day of the "equinox" will not really have equal day and equal night.

Please note that 12 hours of daylight happens on different days depending on how close you are to the equator (the closer, the more ahead of the the Vernal Equinox you will get the true equinox).




02 March 2013

His contribution to the world, WinPlot

http://math.exeter.edu/rparris/images/wpspcover.jpg





Richard Parris, someone who made a difference

As educators, we have a list of colleagues we admire, ones we know from experience make a difference.  Your list probably includes some teachers from your school and maybe from your school district. If you are fortunate enough to be able to attend many professional opportunities, that list includes some people you see only occasionally. And we may admire ones we know only from blog posts or tweets. For me, Rick Parris was in that last category.


Peanut Software

I first encountered Mr. Parris when, in the early 1990's, I was looking for a way to include digitally-drawn mathematical functions in tests and quizzes for a calculus class. I came across WinPlot. It had the nice compromise between small program size and ease of use, and number of features. It became a favorite tool when I was finishing up my graduate work and teaching as an adjunct at a local college, looking to impress the "real" professors. 



When I started my present job, I brought that tool with me, using it when I taught calculus and trigonometry classes. I noticed that Parris listened to feedback from users and made frequent updates. At one time, I wanted to create graphs where the axes are scaled in multiples of pi. So, with a few emails and a couple of weeks, that feature was added. Try doing that with a suggestion for a MicroSoft product. I wrote about using the program in an earlier post.

What is done regularly, is expected

I got used to the regular attention that Mr. Parris paid to WinPlot. I would check every so often to get the newest update. Recently, I noticed that he hadn't updated the program for a while. With a little bit of searching, I found that he has passed away. My heart sank. Someone who created a tool to help students, then noticed that fellow teachers could use it, then made the time over many years to make many changes that others wanted, is no longer with us. He will no longer be able to make WinPlot better. The education world is richer because he cared and poorer now because he is gone.
  

Addendum

I recently contacted a friend of mine who is now at Phillips Exeter where Rick Parris taught. There are no plans for anyone at Phillips Ex to continue with WinPlot or any of the other programs Parris wrote. I do not know how long they will be available (my guess is that the school's IT department will deactivate his account this summer). Even if you have no need now, you will want to download and try his programs here. There is much educational value here. You will find he will help you in your teaching mission.


Update

It has been a year since the death of Mr. Parris and the website is still active. I hope Phillips Ex keeps it going as a tribute to his life.