Chapter 24 Lecture Notes

I’m going to use the “Chapter 24 Resources” document as a basic outline of what I intend to talk about for this chapter. So please start with read/study/practice chapter 24 (first part “Properties of Light”), sections 24.1-24.4, and you’ll want to focus on the problem-solving examples. Please use the “Chapter 24 Resources” document to help you choose what to study in the book. Don’t neglect the student study guide, which I’m pointing out below.

The relevant equations for this chapter are given at the top of page 7 of your formula sheet under the “Light and Optics” heading. Notice that for energy density (utot), it can be calculated in three different ways. You can calculate it as a combination of electric energy density and magnetic energy density or (since these two terms are equal), just doubling the contribution of either electric or magnetic energy density. The units of energy density are Joules/m3.

For the “Intensity of Light” formula, we have two equivalent expressions of intensity, c*utot and Power/Area. If you spread out the energy from a source over a sphere (like starlight spreading out through empty space), you get S = Power/4πr2, but in some cases we may spread out the power over a hemisphere (like a light bulb attached to the ceiling), and then we would get S = Power/2πr2.

Intensity (S) has units of Watts/m2 or Joules/m2-sec.

Also, note the wave equation, which can help you solve problems like Example 24.1.

—Now let’s start solving some problems together. I do not have any problem-solving videos for this chapter, but I think the problems should be fairly straight-forward.

As we would in class, I would like for you to attempt worksheet 24.1. I think it should be a pretty easy warm-up for this topic. Once you have finished it or at least seriously attempted it and gotten stuck, please proceed to the next page to see my detailed solution.

Make sure you are working in mks units for this worksheet. Note that the units of frequency (Hertz) are equivalent to (1/sec) and MHz means MegaHertz. So 88 MHz = 88 x 106 Hz. 


If you have any questions about the way I solved worksheet 24.1, please post to the “Chapter 24 worksheets” discussion forum on the Physics 10164 course shell. I will be checking this forum often to answer questions.

There is similarly a forum for questions about the “Chapter 24 Homework” for the same purpose, and I plan to have two forums for each of the six remaining homework assignments this semester, shared by all three classes, on the same course shell.

Next, I would like to try a slightly more difficult worksheet dealing with power, intensity, energy density and rms electric fields, and that is worksheet 24.2. Please complete or seriously attempt this worksheet as you would try to do in lecture for 5-10 minutes, then when you are ready, check out the completed solution on the next page.

Please refer to your formula sheet for values of fundamental constants and the relevant formulas for this question, and be sure you are working in mks units (so area in m2 instead of cm2). 


If you have any questions about worksheet 24.2, please post to the appropriate “Chapter 24 worksheets” forum on d2l.tcu.edu, and I will respond there.

Our third worksheet is actually a little bit easier, I think. It’s more to give you a feel for how much travel time is involved for light across large distances. Please solve or seriously attempt this worksheet, and then when you have done that, check out the detailed solution on the next page.

http://d2l.tcu.edu

If you have any questions about worksheet 24.3, please post to the appropriate “Chapter 24 worksheets” forum on d2l.tcu.edu, and I will respond there.

I’ll remind you of something I mentioned at least in the MWF classes about this topic, just for your interest. When the Apollo mission astronauts landed on the Moon in the late 1960’s and early 1970’s, they left behind a series of reflectors. We routinely fire powerful lasers toward the Moon to bounce off these reflectors, and by measuring the time it takes for light to make the round trip (down to an accuracy of about 10-11 seconds), we can determine the accurate distance (to the nearest mm or so) to the Moon over time. This “laser ranging” experiment has showed over the past few decades that the Moon is receding from the Earth at a rate of about 3.8 cm per year!

If you would like to learn more about this topic and how it affects our calendar, how it affects the Earth’s rotation and tides, etc., I encourage you to read the wikipedia article on this topic:

https://en.wikipedia.org/wiki/Tidal_acceleration

Obviously, I’m not going to be asking about the details of this on our 3rd exam. Every once in a while, I just like to remind you that there are some cool things you can do with Physics concepts, and they almost always involve Astronomy.

For our final worksheet in this part of the chapter, I am asking you to again look at the concepts of Power, Intensity, Energy Density and rms Electric Field in worksheet 24.4. Note that this worksheet presents the “hemisphere” case for a source of energy instead of the “uniform radiation in a sphere” case. I talked about the difference between these two cases back at the top of page 2 of these lecture notes.

Please solve or seriously attempt worksheet 24.4, then check out the detailed solution on the next page when you are ready.

http://d2l.tcu.eduhttps://en.wikipedia.org/wiki/Tidal_acceleration

If you have any questions about worksheet 24.4, please post to the appropriate “Chapter 24 worksheets” forum on d2l.tcu.edu, and I will respond there.

For the other major section in Chapter 24, I encourage you to read/study/practice sections 24.5 and 24.6.

The first of the two topics to cover in this part of Chapter 24 is Doppler shifting. Our formula for this concept is near the top of page 7 of your formula sheet. Note that there is a “frequency” and “wavelength” version of the Doppler shift formula. You will likely find the frequency version easier for use when solving the 2 worksheets that are coming your way, but the homework uses the “wavelength” version more naturally. You can solve any of these problems with either version of the formula, of course, but one way will usually be much easier depending on what quantities you are given.

So, with that said, let’s move to worksheet 24.5. PLEASE SOLVE EACH PART WITH FOUR SIGNIFICANT FIGURES. The tricky part of this one for some people seems to be figuring out what is relative velocity. Easiest for me to to consistently assume v(relative) = v(source) - v(observer), and be sure to use consistent sign conventions (for example, motion to the right is positive, motion to the left is negative).

When you have solved or at least seriously attempted this worksheet, please take a look at my solution on the following page.

http://d2l.tcu.edu

If you have any questions about worksheet 24.5, please post to the appropriate “Chapter 24 worksheets” forum on d2l.tcu.edu, and I will respond there. I also would like to point out that this same problem is in your WileyPLUS homework for chapter 24 as problem #38. Look there for a brief tutorial and a more detailed discussion of the solution.

The next Doppler shift problem is a little tricky in the wording. Notice that the problem gives you the source frequency and the DIFFERENCE between the source and observed frequencies. See if you can work out how to solve for the speed of the car. Once you have solved or seriously attempted worksheet 24.6, look at the next page for the detailed solution.

http://d2l.tcu.edu




If you have any questions about worksheet 24.6, please post to the appropriate “Chapter 24 worksheets” forum on d2l.tcu.edu, and I will respond there. There are a couple of similar problems in the WileyPLUS homework assignment as well that you may wish to try if you had trouble with this one.

The final topic in Chapter 24 involved Polarization, which is conceptually pretty weird but mathematically pretty easy to handle.

Light from most sources is unpolarized. Polarization refers to the plane of orientation of the electric field of the traveling electromagnetic wave. If all of the waves from a light source have their electric field oriented in the same way (in the example below, vertically up and down) then we say that light is polarized. If the waves have random orientations, the light is unpolarized.

A polarizing substance can be designed as a series of very long, skinny molecules all oriented in the same way. These molecules have a free electron that is free to wander up and down the molecular chain, and it acts as a miniature antenna.

If an electric field is incident on the molecule and oriented in the same plane as the molecule, the electron will oscillate in response to the field, generating its own electromagnetic wave that cancels out the incident wave. If the molecules are perpendicular to the incident wave, then the incident wave passes through the material without being affected.

http://d2l.tcu.edu

So in the end, only the portion (or component) of the electric field of the incident wave that is perpendicular to the molecules will pass through.

So you can think of a polarizer like a narrow hole in a wall, as the book analogizes in the figure above. If the wave oscillations are favorably oriented with the hole, then the wave passes through without a problem.

If unpolarized light passes through a polarizer, the result is simple: the output is light with exactly one-half of the original intensity, and that light is polarized parallel to the polarization axis of the material. Only the electric field component that isn’t blocked by the polarizer gets through, so the resulting wave is polarized.

If the wave is only partially oriented with the polarization axis, then the intensity is reduced by a factor of cos (theta) squared, which is a derivation you don’t have to worry about.

So like I said, conceptually, it is challenging, but mathematically, the formulas are pretty basic. If you haven’t already read through the examples and applications of this concept in chapter 24.6, I encourage you to do so. This is a pretty cool application of what we have been learning.

Now it is time for our last worksheet of the chapter, applying our two formulas for polarization. Please solve or seriously attempt worksheet 24.7, and when you are done, check out my solution on the following page.

If you have any questions about worksheet 24.7, please post to the appropriate “Chapter 24 worksheets” forum on d2l.tcu.edu, and I will respond there. The worksheet is very similar to one of the examples in the chapter.

Finally, some specific example problems from recent old exams that may help you practice if the worksheets and homeworks aren’t enough. Please reference the following:

Properties of Light problemsSummer 2019, Exam 3A, #1Spring 2019, Exam 3A, #1Spring 2019, Exam 3B, #1Spring 2019, Exam 3D, #1Summer 2018, Exam 3, #1Spring 2018, Exam 3A, #1

Doppler Shift or Polarization problemsSummer 2019, Exam 3B, #1Spring 2019, Exam 3F, #1

This concludes my lecture notes for Chapter 24. I hope you found these somewhat in the ballpark of the usefulness of my lectures. Now, of course, it is time for you to get going on the Chapter 24 homework.

As always, I hope you will solve or seriously attempt each problem before asking for help. I will be checking the “Chapter 24 homework” forum on our course shell occasionally and contributing helpful comments in response to any questions you may have about the homework.

I wish all of you much luck and little stress as we embark on this strange online teaching experience!

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