A few months ago, Prof. Keith Schwab brought visiting students and teachers from Navajo Preparatory School to tour some of the IQIM labs, listen to some quick lectures on optics, and talk to scientists. Since this opportunity was only allowed to the one carload that made the 11.5 hour drive from Farmington, NM, everyone involved agreed that we could reach far more students if the IQIM sent Caltech students there. Ana Brown and I both enjoyed speaking with the visiting students and teachers, and responded enthusiastically when Prof. Schwab offered to send us. My enthusiasm momentarily dimmed when I realized our trip would be occurring in the dead of winter and it was projected to snow while we were there (having only lived in northern and southern California, let’s say I have a heightened sensitivity to weather), but I excitedly spent thanksgiving putting together demonstrations with supplies I found in my closet and garage. I’ve always enjoyed talking about applied math, science, and engineering to anyone, especially anyone young enough to have only heard “math is boring” or “science is too hard” few enough times I can convince them otherwise. Navajo Prep seemed ideal for this, since the school prepares the students well and sends over 95% of the students to college, and is working to increase student interest in math, science, and engineering.
Panorama from the center of Navajo Prep
With a suitcase half full of clothes and half full of tools and hacked-together electronics, I was picked up from the airport, and arrived at the school in the afternoon the Monday after Thanksgiving weekend. While Monday was spent arranging which classes I would attend, and what topics I would discuss, my second day involved a trip with the school’s outreach coordinator and Cody, one of the two students who visited Caltech, taking a tour of some of the local highlights, including a traditional Navajo lunch (steam corn stew, roast mutton, and I even tried ach’ii”) and toured the remnants of the cliff dwellings at Mesa Verde, about half an hour from the school. Exploring a region with such a rich history and discussing it with my hosts, who are descendants in part from that history was an incredible experience.
Rooms at the Oak Tree House at Mesa Verde
On Wednesday, I began talking to the freshman physics classes about optics, intending to discuss the properties of light, like frequency, speed, wavelength, velocity, energy, and momentum, but to give some context I began with a historical summary of discoveries in optics. I know I was surprised when I was preparing, so you might enjoy answering the same questions that I asked the class. Take a second, and guess when you think the first lenses were made and when wearable glasses were first used. (After you think you have a guess, scroll to the bottom to see how you did.) When I realized that the class was more interested in seeing rather than hearing about optics, I skimmed over what I’d prepared in order to spend more time on the demonstrations where I showed refraction in glass and explained how that can be derived from assuming a different speed of light in the material. We found lenses for the students to manipulate/play with, and even though historically there were about 300 years between invention of glasses (and the proliferation of lens-making) and the invention of the telescope, some of the students unintentionally built telescopes after taking a second lens from their friends and were shocked to hear that what they had just made was better than the one Galileo used to first discover the four largest moons of Jupiter.
Measuring focal lengths and observing lensing with a drop of water on a glass slide
We also demonstrated double slit diffraction and calculated light’s wavelength for three different laser pointers to within 5% accuracy using only a tape measure, a post-it, and a knife. I decided not to bring a demonstration to measure the speed of light with a laser, a few mirrors, a computer fan, and a reverse-biased photodiode hooked up to an old speaker, because I couldn’t get the fan to spin fast enough to get a reasonably short delay length. (From that can you guess what my set-up was?) On Thursday, Ana and I gave a similar lecture to a different pair of 90 minute freshman physics classes, and spent the other periods talking with math classes. In calculus, I described the different kinds of math classes offered in college, their applications, and their connections to each other in an attempt to give more meaning to the course titles they would no doubt be reading next fall. In geometry and trigonometry I answered the perennial high school math question: “when will we ever use this?” by talking about some applications in geometric optics.
Since I figure you readers like thinking about this sort of thing, I’ll elaborate: I started with the fact that a light beam’s incident angle (measured from the perpendicular of a surface) is equal to its reflected angle. This means that light propagation, like much of (but not all of) physics, is reversible in all but a few specific cases. As a result, light generated at or passing through the center of a circle is reflected off the circle back to the center. An ellipse has a similar property where light through one focus is all reflected to the other. Try deriving that from the fact that an ellipse is defined to be the set of all points where the sum of the distances to the two foci equals some fixed constant. In the lecture, I then used the fact that a parabola is the set of all points equidistant from a point (the focus) and a line (the directrix) to show that light from the focus is reflected off the parabola and collimated (focused at infinity).
Ana brought some IQIM hats and shirts, which the freshman physics classes seemed to definitely enjoy when we met with each class for 40 minutes on Friday.
One of the four freshman physics classes we got to spend time with
I tried to give them an impression of what we do in the IQIM, but I had a hard time giving a satisfactory explanation of the significance of quantum information, and Ana easily convinced me that it would be more engaging to use the 90 minute introduction I had already given them on optics to explain and describe solar energy, since many buildings deep in the Navajo reservation are off the power grid. There are also plans to construct a large solar power plant on the reservation that will be much cleaner than the three local coal power plants in the region.
Action shot during the lecture on solar
Ana and I also spoke to the senior seminar, which contained the entire graduating class, where she talked about the difficulties transitioning to college experienced by some of her friends in college who were from the Navajo reservation. She gave such great advice on applying to schools, applying for fellowships, and developing a healthy work/life balance, that the only thing I felt like I could contribute was some advice on picking a major (since I’ve picked about 4 different majors), where I described the difference between science and engineering, and talked about different fields within each. I loved how truly helpful I felt when so many of the students told us that they either found certain pieces of advice to be useful, thanked us for introducing them to an idea they hadn’t heard of, or asked us to come back soon.
Occasionally a student asked what I personally do, and their curiosity was rewarded with an explanation that lasted as long as they were interested. The shortest lasted two sentences and the longest explanation (given to a calculus class of 5 people) involved 30 minutes with my laptop out showing all the steps I take to fabricate nanoscale devices to trap light in almost a cubic-wavelength volume in proximity to an “optically interesting” rare earth ion which my advisor and I hope will provide a viable quantum optical memory. (Here‘s a little more about our work.)
In the evenings we cheered for the school’s basketball team, had dinner with some of the students and teachers, and discussed the school’s science curriculum and science fair projects. Ana and I consulted on a solar water heating project some of the students were working on, and, after the students all went home for the weekend, I even spent 2 hours in 17ºF weather the last night calibrating an 8″ diameter Schmidt-Cassegrain telescope that had been donated to the school. Compared to Pasadena the viewing was spectacular, and I could easily spot galaxies, nebulae, and discern stripes on Jupiter and the four Galilean moons. I can only expect that some of the students I met will be as excited as I was.
From wikipedia: “The earliest known lenses were made from polished crystal, often quartz, and have been dated as early as 700 BC for Assyrian lenses” and “Around 1284 in Italy, Salvino D’Armate is credited with inventing the first wearable eye glasses.” For anyone who’s interested in the history of science, I’d suggest you check it out.