Lec 7
“The test of a good teacher is not how many questions he can ask his pupils that they will answer readily, but how many questions he inspires them to ask him which he finds it hard to answer.” Alice Wellington Rollins (American writer 1847-1897)
Links for this lecture: https://en.wikipedia.org/wiki/Mode-locking http://mathlets.org/mathlets/series-rlc-circuit/ https://www.geogebra.org/m/FVqeYkye
Lecture overview for today: We will review two topics then cover two more topics about which you will complete a worksheet. The topics are: asking pertinent questions from a light clock prompt and adding harmonic functions to describe the output of a grating. Answers to this worksheet are discussed after the worksheet is completed.
Lab overview for today: In the lab you will explain your model and procedure sections to the next group. I too often see student showing graphs of their data and talking about conclusions. Please don’t do that and just follow the instructions found in the evaluation form.
Review the photodetector, phasors in circuits, and pendulum prompt from last week. After a week to think about these topics you may now have questions.
Review photodetector: -Talk about how the capacitor integrates (review the PLC discussion) or adds together the charges. It may be best to have the photocurrent go through a resistor and integrate the voltage across the resistor rather than the current since it is conceptually difficult to see how the charge from the detector would accumulate on a capacitor.
-Put numbers into the photodetector problem. The distribution for integrating over 1 ns is 1.0 +- 0.1 V. Find the mean of 100 such measurements (add 100 random samples from the distribution and divide by N) which yields 1.0+-0.1/Sqrt[100]. If you integrate over 100 ns the distribution is 100 ( 1.0+-0.1/Sqrt[100]) V= 100.0 +- Sqrt[100] 0.1 V. The spread in voltages increases by Sqrt[N] but the percent variation goes as Sqrt[100] 0.1/100 = 0.1/Sqrt[100].
Talk about the signal being a percent of the total rather than an absolute number. If your signal is absorption then a certain number of atoms with absorb a percent of the incident photon flux rather than an absolute number of photons. Draw the analogy with cars crossing a line in 10 secs vs 1000 secs. The number of cars increases by 100 while the std dev only increases by sqrt[100].
Review phasors in circuits: -show animation of phasors for a circuit. Emphasize how Kirchhoff's law is satisfied. http://mathlets.org/mathlets/series-rlc-circuit/
Review questioning with the pendulum prompt:
-Causal/creative: could this be done with standing waves? Here is an example using EM wave. Note in the upper animation the standing waves are superimposed while in the lower they are added.
https://en.wikipedia.org/wiki/Mode-locking
New content: Phasors in multiple slit diffraction.
In class worksheet questions: 1.) Where is the harmonic wave crest, which was at the origin at t=0, located when t = t0 for Cos[kx-wt]? 2.) How what is the difference in distance between wavecrest for these waves Cos[kx-wt+delta] and Cos[kx-wt]? 3.) Explain how the grating phasor diagram differs from the circuit phasor diagram.
Consider a harmonic wavefunction for EM waves Cos[kx-wt] where k =2 Pi/lambda and w = 2 Pi nu.. This can be rewritten using lambda nu = c where lambda is the wavelength, nu the frequency, and c the speed of a wavecrest. Cos[ 2 Pi nu x/c - 2 Pi nu t] = Cos[2 Pi nu (x/c-t)] =Cos[2 Pi nu/c (x-ct)]. Let the phase phi = 2 Pi nu c (x-ct). For fixed phi different values of x and t are possible. This indicates a that fixed phi represents a traveling wave.
Show the animation of phasors related to a grating found here https://www.geogebra.org/m/FVqeYkye
Explain: What harmonic functions are being added for waves from different slits? What is kx? How do phasors show this?
New content: questioning on a light clock.
In class worksheet questions: 1.) Write three questions on the light clock prompt only in the modifying category.
Answers to worksheet questions:
Topic 1: Phasors description of a grating:
1.)Set the phase =0 and solve for x as a function of t to see where the crest is located at a given time.
ANS: k x - w0 t =0 . Solve for x = w0 t/k
2.) delta is the phase shift of one wave relative to the other. Set it equal to k X where X is the phase offset. This is a distance of delta/k = 2 Pi radians /delta radians times lambda. If delta = 2 Pi then the offset is one wavelength. Ans: k dx = delta, where delta is in radians. Solve for x = delta/k = lambda delta/2 Pi. Note that delta/2 Pi is the fraction of radians that the phase shift delta gives. Therefore 2 Pi radians times this fraction is the fraction of a wavelength that delta radians corresponds to.
3.) Time is the variable in the circuit phasor diagram of V=V0 cos[omega t], while the phase shift per phasor is plotted as the independent variable in the grating animation. This animation was made by mathematicians who don’t worry about what the symbols mean. A physicist would have plotted the distance along the screen illuminated by the light. To convert the phase difference between phasors to this distance note that this phase difference phi = m lambda = d sin[theta]. Also theta is approximately equal to distance along the screen/distance from the grating to the screen = y/D. Therefore the phase difference between phasors is phi = 2 Pi d sin[theta]/lambda = 2 Pi d y/D . The horizontal axis would then be transformed using y = D phi/(2 Pi d).
Topic 2: questions about a time clock:
Sketch the light clock. Indicate how it shows that time in a moving frame appears to move slower than in the rest frame of the clock. This is like having a jar of mosquitoes which live for a short time. Have two jars at rest separated by a distance D and a another jar move at speed close to that of light. Let the eggs hatch when the moving jar is by one of the stationary jars. More will be alive in the moving jar when it reaches the other jar.
Modifying questions: -what happens if the clock accelerates? -what happens if the clock is along the direction of motion?
“The test of a good teacher is not how many questions he can ask his pupils that they will answer readily, but how many questions he inspires them to ask him which he finds it hard to answer.” Alice Wellington Rollins (American writer 1847-1897)
Why didn’t you ask these questions that your instructor would find hard to answer in PH300?
What do you think is the biggest hindrance to critical thinking (asking pertinent questions)? a.) You don’t care because the things being taught are not important to you. b.) You don’t have the time to critically evaluate the material, due to some deadline. You then rely on heuristics (System 1 thinking) such as work backward from the answer to find out how it was derived. In business it is often the case that the most important thing is meeting a deadline rather than the quality of the work. Mines is good at training students to get the work in on time with less of an emphasis on truly understanding it, in my opinion.
Appendix: Here is an example of the lack of critical thinking. Writing code: more important to get it to work than think critically about what assumptions are built into it. https://www.theatlantic.com/technology/archive/2017/09/saving-the-world-from-code/540393/ For Lamport, a major reason today’s software is so full of bugs is that programmers jump straight into writing code. “Architects draw detailed plans before a brick is laid or a nail is hammered,” he wrote in an article. “But few programmers write even a rough sketch of what their programs will do before they start coding.” Programmers are drawn to the nitty-gritty of coding because code is what makes programs go; spending time on anything else can seem like a distraction. And there is a patient joy, a meditative kind of satisfaction, to be had from puzzling out the micro-mechanics of code. But code, Lamport argues, was never meant to be a medium for thought. “It really does constrain your ability to think when you’re thinking in terms of a programming language,” he says. Code makes you miss the forest for the trees: It draws your attention to the working of individual pieces, rather than to the bigger picture of how your program fits together, or what it’s supposed to do—and whether it actually does what you think.
Alums have told me that the most important aspect of their work is getting the job done on time. Not necessarily of get it done perfectly. Does that sound like your homework assignments?
