Written HW due every week. 32.17, 32.47 Due Fri Jan 18

1. Physics 262Website:http://panda.unm.edu/Courses/Thomas/Physics262/phyc262.htmlYou will want to get an iClicker and Mastering Physics. Course ID MPTHOMAS40380Register your iClicker with your banner ID. Clickers get 1 pt for any answer, 2 pts for correct answer!SI Jonathan GrossSI sessions M & T at 9, Th at 10

2. Written HW due every week. 32.17, 32.47 Due Fri Jan 18 Some stuff in physics is best memorized. Remembering some basic facts or equations helps you think better, because you can draw on those tools. Example: What is the relationship between wave speed v, frequency f, and wavelength ? a) v = f/  b) v = f  c) v = f d) v = f  e) None of these

3. More waves • When a wave reflects off a fixed end, the reflection • A) is inverted • B) is not inverted • C) vanishes completely

4. The electromagnetic field supports waves.This is usually “explained” by induction:Changing E field “causes” B fieldChanging B field “causes” E field We will see in a month that there is a better explanation for these waves.

5. Electromagnetic “Discontinuities” Must Propagate at a speed

7. Our wavefront satisfies both “Gauss’s laws” because there is no enclosed charge or current, and fields on opposite sides of the box are the same.

8. There is a changing B flux as the wavefront moves by. This changing flux must be equal to the line integral of the E field. Only the back edge (gh) contributes to this line integral.

9. There is a changing E flux also. This gives another reqd relation between E and B.

10. Clarification:4 % problem session bonus is for going to 1 per week(Total of 14 or more.) • Last time: Maxwell’s eqns support spatially varying E fields if: • The fields move at speed c = 3x108 m/s • There is an associated B field, B=E/c We call waves that have the same E, B at every point in a plane “plane waves” Some plane waves are sinusoidal. Maxwell’s equations also allow for non-plane waves. (Because they are linear, any sum of allowed waves is also allowed. Non-plane waves can be mathematically shown to be sums of plane waves.)

11. So these waves can exist. What can make them? Classically, an accelerated charge makes an EM wave.

13. Consider the E field described by the following equation What is the direction this wave is moving in? Toward +x Toward -x Toward +y Toward -y Impossible to tell

14. What is the associated B field of

15. For a given sinusoidal plane wave, you need to be able to tell the direction of propagation and the direction of the associated B field. More about k and  What is the wavelength of a sinusoidal wave with wavenumber k? 1/k (2)/k 2k None is correct

16. HW Due next Friday Jan 25 33.57, 33.61Last time: • Understanding sinusoidal plane wavesFind direction of wave propagationUnderstand allowed polarizationsFind associated B field: cB = EFind wavelength, frequency• Poynting vector SDirection = propagationMagnitude is energy per time per areaP = S/c is momentum per time per area = pressure

17. A few loose ends:1. What is relationship between k and P = S/c. Would this be different if light were particles?(This is just for fun…)

18. The Poynting vector S is proportional to E2 (and/or B2) Consider energy conservation to answer this question: How does E depend on r, the distance from a point source of radiation? E ~ r E ~ 1/r E ~ 1/r2 E ~ ln(r) E is independent of r

19. You should also remember the wavelengths of visible light, and the very approximate boundaries between the other EM radiations. How? Gamma rays are the size of a nucleus X-rays are the size of an atom Visible = 400-700 nm Microwaves fit in the oven IR is between microwave & visible Radio: figure it out from the frequency. KUNM 89.9 MHz Light (em radiation) of wavelength 2 microns is A] gamma ray B] x-ray C] visible D] infrared E] microwave

20. What is the approximate wavelength of KUNM? A] 3 nm B] 3 microns C] 3 mm D] 3 m E] 3 km

21. Light in materials. Replace 0 and 0 with  and . Usually Km = 1, so it is the dielectric constant K that is important. n is the “index of refraction”

22. Parting comment:Maxwell’s equations predict a wave satisfying the wave equationIn this equation, there is no reference to the speed of the observer or the source of the wave. Other waves are much more complicated: for example, consider sound waves on a train flatcar. We need to have a different speed upwind & downwind. Perhaps Maxwell’s equations are only approximately correct?? Maybe our motion on the earth (around the sun & galaxy) is slow enough (compared to c) that we don’t notice the differences in the upstream and downstream speeds of light?You can see that, if that were so, the EXACT Maxwell equations would be ugly, not neat, beautiful, elegant, simple, as they are.Does this matter? Maybe the universe is not so neat!Albert E., yours truly, and God all favor neatness & elegance.

23. Chapter 33 Nature and Propagation of LightWavesWavefronts - “locus of all points at the same phase”Here “phase” means that, for a sinusoid, the argument would stay the same. (“phase” = argument of sinusoidal function)It’s easiest to think of wavefronts as simply the crests of the wave.

24. Rays are imaginary lines along the direction of wave propagation. What is the relationship between rays and wavefronts in vacuum?A) they are parallelB) they are perpendicularC) they are at 45° to each other

25. Reflection: light bounces off a surface (e.g. mirror, or glass)Refraction: light bends as it enters a material with a different index(I.e. a material in which the speed of light is different!)Law of reflection (memorize) Law of refraction- “Snell’s law” (memorize) Angles are measured to “normal” Snell predates Newton!

26. When a beam of light enters a piece of plexiglass, what will be its path? (np > 1)

27. The wave equation is time-reversal symmetric. A laser in air shines a beam of light that hits a diver, rightmost path. The diver has a laser pointer, and wants to hit the air laser. What direction should he point it? Or choose D: no direction will work.