Online chat

If you need more instant gratification than email or facebook messages can provide: (a) I usually leave my facebook chat on, (b) I'll start to leave my google chat on more regularly, (c) you can also find me at uaphysics on AIM.

Don't worry that you are interrupting me. If I'm not available, I'll turn it off, or just not answer :-)

HW2 hints

UPDATE: on number 3, you should get about 2.25m and 2.1m (not 2.6m and 2.1m).

Some stray HW2 hints:

(1) Draw a normal to the prism surface at the incident and exit points. Let θ₁ be the incident angle (relative to the normal) and θ₄ the exit angle. Let θ_2,3be the refracted angles relative to the normal on the incident and exit sides, respectively. The deviation angle is then θ₁-θ₂+θ₄-θ₃.

Use the triangle formed by the incident and exit rays and the apex (angle φ), all the angles sum to 180 deg. Apply Snell's law, and you're basically done. About 4.6deg.

(2) Use (3.70) in the text. Presume the 2nd term under the radical is small compared to 1 (try to justify this), and note sqrt(1+x)~1+x/2 for x<<1.

(3). The lateral position of the object is unchanged, only the depth is different. To see this, think about rays emanating from the object at the bottom of the well and trace them to the observer's eye. The apparent position is where the ray reaching the observer would extrapolate back to the horizontal position of the object.  About 2.25 and 2.1m, respectively.

(4). Check out this figure. The angular rotation rate of the earth is ω=2π/86400s, and the angular deviation is δθ=ωδt. Double that for sunrise and sunset. About 160s.

(5). Use the result of problem 1, noting by symmetry that θ₁=θ₄ and θ₂=θ₃.
(6). Carry the sums through (i.e., you needn't bother just keeping the first term), but approximate to first order 1/(1-x)~1+x and sqrt(1+x)~1+x/2 for x<<1.
(7). We'll do this one in class on Tuesday. The time it takes to cross a distance Δy in air is Δy/c. Crossing the same distance of glass means a time of nΔy/c. The difference between the two is the phase lag the observer sees, basically an offset in the observer's clock. Without the plate, the wave would be exp(iωt - y/c) to account for the frequency and propagation delay across a distance y.

(8). We'll do this in class. Re-write n sin(θ) as a cross product on each side of Snell's law ...

Homework 1 solutions

Here you go.

Homework 2 is out

I know you're excited. Due 27 Jan before midnight.

Rayleigh Scattering

Here are some very short notes which corroborate our derivation today.
And, here is something much fussier which ends up with the same result.

Aside from the fact that your textbook says the same thing, of course, but if it is on the internet it must be true.

Both of these are more than you need to know. The point of my posting them is to give some rationale for my writing a whole bunch of my own notes on radiation & scattering. Every treatment I found was either far, far too mathematically fussy to justify the only-approximately-correct result, or too hand-waving to be of much use. This is particularly true if you want to go further and derive black body radiation - the favorite derivation involves densities of states and mode counting, which is just unnecessarily obtuse. (FWIW, the Feynman lectures do a brilliant job, though you'll have to skip across all three volumes to get the details, and it is Purcell's ingenious derivation of the Larmor radiation formula that I followed in class.)

Our approach was to take the middle ground: put in just enough physics to be dangerous, if we really need to be, but recognize that the basic question is "why is the sky blue" and not "how many watts are scattered per steradian per unit wavelength." And, the answer to the simple-sounding question is quite a bit more complicated than you thought, right? Only answering the more complicated-sounding question can obscure the fundamental understanding: we could have derived the scattering cross section in hideous detail, that doesn't tell you why the sky is blue. We'll come back to the complicated question later.

Anyway: the main point is that we'll put in as much physics as we think we need, and not any more. If you want a 10% solution, that is a much different problem than wanting a 1% solution, so pick the battles that matter.

(Recall what we did today: after determining the radiated power for an oscillating charge, we found the radiation reaction (Abraham-Lorentz) force that must be present (damping). Then we presumed small damping, so all we really did was figure out how a bound charge could be approximated as a simple harmonic oscillator with radiation damping, equivalent to an RLC circuit.)

Hecht errata

The list of errors Andrew pointed to is here.

In addition, Andrew noted

There appears to be an error in Hecht's book on page 651 in the magnetic equation of telegraphy (A1.20). The first equality sign should be a subtraction operator. This isn't noted on Chris Mack's errata sheet.

I'll keep updating this post as we find more things. The solutions manual that accompanies the book is rife with errors, it is probably a losing battle to try and write all those down for the few (or none) of you that have it.

Animations of moving charges

The E field from moving charges, applet.

Another timely XKCD

It wasn't like this, right?

Today & Thursday's lectures

Today's discussion of accelerated charges and radiation, and pretty much all of what we'll cover next time, can be found in these previously linked notes.

Motivation

Brilliant. You should have no trouble finishing your reading now.

Wolfram Alpha

Wolfram Alpha. Physics, math, etc. Incidentally, it will do definite integrals numerically, solve cubic equations, and other things useful for your upcoming homework sets.

There is an iPhone app.

Supplemental notes

My PH102 notes, which includes a small bit of basic optics. (basic review)
PH253 notes on radiation and scattering. (supplemental for next week's lectures)

UGrad research conference

RESEARCH AND CREATIVE ACTIVITY CONFERENCE APPLICATIONS — Faculty are requested to remind undergraduate students of all majors that they are invited to enter UA’s annual Undergraduate Research and Creative Activity Conference scheduled for April 11 at the Bryant Conference Center. Students can compete for cash prizes and earn practical experience in defending or performing their work before judges. To participate, undergraduate students must register their projects by submitting application forms and abstracts describing their projects by March 7. Visit http://www.osp.ua.edu/UndergradResearch.html for an application and details.

HW 1 is out

Here is your first homework set. It basically covers the prerequisite material - while you may not know immediately how to do all of these problems, they should not be terribly mysterious after reading Ch. 2 and 3 of the Hecht textbook.

Due 20 Jan 2011 at 11:59pm; we will cover some of these in class during next week's lectures.

Slides for lecture 1

Here are the slides for the first lecture. They contain the basic course information, a quick review of vector calculus, and some supplemental information. The last ~half of the lecture will be on the whiteboard, a "review" of Maxwell's equations in free space.*

It will be presumed that most of Ch. 2 in the Hecht textbook (wave motion) is somewhat familiar to you. The first HW set, posted shortly, will make sure of this.

The second lecture will cover electromagnetic waves in more detail, and start our discussion of radiation. The third lecture will cover radiation from accelerated charges (dipole, synchrotron, thermal), and scattering & dispersion. At this point, you will know why the sky is blue.

*It will be review if you have had PH331 or ECE340. If you have only had PH106 it will only be review for a little while, but you'll be OK.

Syllabus, schedule

Some general course information:

PH syllabus, ECE syllabus (they are essentially the same)
detailed course schedule (duplicated on the course calendar)

Welcome to optics!

This is where you will find all the information you need for PH495/ECE493/ECE593 for the Spring 2011 semester.

In another day or two, I will have the syllabus, schedule, and some other details posted ... for now, you can review the course calendar, embedded at the bottom of the page or using the link on the right.