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.

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.

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).

His contribution to the world, WinPlot

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. 

My School has a Fantastic IT Department

  

Do they work with you or against you?

Networked computers are a fact of life in the modern classroom. However, many schools put barriers in the way of a teacher who wants to try new software or add new features. Most schools I know of have a "locked-down" policy for their school issued computers. Any new software or modifications of features requires official permission. Some schools will process requests with glacial speed and others schools will  so in a few days. One district in my area erases and then completely re-images the hard-drives each evening. I know of one teacher who was almost fired because, in his enthusiasm to share with his students the neat things that could be done with an iPad and Vernier's Video Physics software, downloaded a $3 app without prior approval (fortunately his principal came to bat for him, but I am sure that there is a "letter in his file").

Each time I hear about another school's restrictive policies, I am grateful for my school's IT staff.

Trust the Teachers

I have just finished installing Linux on my newly-issued MacBook. This is the third school-issued computer that I have done this on. Each time I have asked permission from the IT head, expecting a polite refusal, but the only restriction I have received is that they would not be able to give me support for it. It does help that the IT head is something of a penguin-head himself and knows that there is a world beyond the Win-Mac duopoly. 

Why Linux?

As someone brought up with the Unix ethos of hack-able software (in the original sense), I have valued FOSS (free and open-source software). Linux is built on that ethos. I try to show my classes that philosophy also. When we do linearization of data using spreadsheets, I demonstrate with Gnumeric. When we study sound, I show them what Audacity can do. If I have enough time, I like to use Audacity to show how to rebuild a sound using only sine-waves (a reverse FFT). To do that, I had to take the source code and make a minor modification. Had that code not been available, I would be at the mercy of what the programming team thought I wanted to do. Here is the ethos at work; here is my work, use it, improve upon it if you want. 

With Freedom comes Responsibility

Since I am trusted by my school's IT head, I do not want to betray that trust. So there are certain things that I could do that I will not do with school computers. I would love to jail-break my iPad to circumvent Apple's "do it our way or no way" mentality, but that might expose our school to legal problems. The same with using "abandonware". OK, once I used some cracking software on my laptop to recover a forgotten administrator password, but it was with an unofficial blessing, otherwise my computer would have to have been completely re-imaged, wiping out all the added programs and customizations.

It is more work for them

I am sure that a totally locked-down approach to school-issued technology would make my school's IT department's job much easier. But they have adopted the philosophy of letting the teachers deciding how they want to use their technology. We are then able to show what we have discovered with not only our students but also with fellow teachers. This policy lets us be more spontaneous and innovative teachers. For that freedom, I am thankful.

Why don't you have a New York Public Library card?

Why don't you have a New York Public Library card?

 Ebooks are becoming a feature in the classroom. And libraries are a good source. While my local public library system has made it easy to get ebooks (and to search for dead-tree books and to have them sent to my nearby branch), it is somewhat limited. At a recent meeting of the Western New York Physics Teachers Alliance, I learned that I have another resource.

Do you live in New York State?

If you live in NYS, you are eligible to get a New York Public Library card. While you may not get to visit an actual branch, you can download from their large ebook collection. The shot below is the beginning from a search for "quantum". Many books are on the graduate student level, so the selection is deep.

The actual process of getting the card will take a few weeks.  You first request one on their website and wait a couple of weeks until it arrives in the mail. You then need to send in a picture that proves you reside in NYS (unless you want to drive to Gotham and visit one of their branches). Wait a few days and when you get an email confirming your acceptance, you are set to go. It is free, so why are you waiting?

If you are an iPad user, the Overdrive Media app allows you to access the NYPL and read books on that device.

The RaspberryPi is one of those things that captures the imagination of some people. While many people are using it for useful purposes, I have decided to use mine for nefarious ones.

I have set up a Pi on our school's network, but in the office of the faculty member who has the responsibility for training the rest of us in technology use. I will sneak into his office early Friday morning and attach some speakers to the Pi.

Since I can access this computer from my laptop, I will start to play some songs from the Bob Rivers site at what I hope will be a semi-inappropriate time.

The Roller Coaster and the "Natural Path"

A classic example for HS physics teachers when discussing circular motion is the roller coaster loop. And the classic difficulty is getting students to understand the role the track plays in exerting force on the roller coaster car. To help with that, I have developed the idea of the "natural path".

After the basic discussions of circular motion and the emphasis that the force needed for circular motion  is not a real force, but the result of other real forces (I seldom call it centripetal force), we go to the roller coaster. However, I start with a typical loop cut in half vertically. We discuss what path a car would take when it came to the top of the loop and flew out into space. We get the typical projectile path. We draw one for a car moving at high speed and then another for one moving at low speed. I call those the "natural paths" that the car wants to follow.

I then draw in the rest of the coaster loop. We look at the high speed case and note that the natural path lies outside the loop. What prevents the car from following its natural path? The track. It must exert a force downward on the car to make it move in a circle.

We then look at the low speed case and see that the track must exert an upward force to keep it moving in a circle. We discuss what a rider would feel for each of these cases, with my in-class examples all starting with a roller coaster engineer specifying the force she wants a typical 75 kg rider to feel and then calculating how fast the car has to be moving to satisfy that requirement.

So, what will you feel?

Now comes the task of getting students to understand what the roller coaster passengers will feel. It starts with what they are feeling now. We talk about the forces they feel as they are sitting on the classroom stools. We decide that "normal" is when they feel the seat pushing up against them with a force equal to their weight. It usually takes some more discussion to get them to realize that they would feel "normal" when something is pushing against their butts, whether is it up or down. So, when the track (and thus the seat) is pushing with a force against your butt, you feel attached to that seat; you don't feel like you are falling. If that seat no longer pushes against your butt or is even pulling your butt down, you no longer feel attached to that seat; you feel like you are falling.

For advanced students

If you have students with a good calculus background, you can have them compare the curvature of the natural path to the curvature of the loop. And they can then calculate the force exerted by the track from the differential equation F=dp/dt.