1. Friday(03/05): Ch.24 - Intro. to Electromagnetic Waves

and the Spectrum. HW: Read and Study pages 722-27, then solve

problems 1, 2, 7, and 8 on pages 745.

2. Monday(03/08): Energy of Electromagnetic Waves, The Doppler

Effect of Electromagnetic Waves, and Polarization. HW: Read and

Study pages 728-29, then solve problems 14, 15, 16, and 20 on

page 746.

·        Report to 1^st per. class; then, ESE and ESOL students report to their extended

         time testing locations for the second session of the Reading FCAT; and grade 11

         students report to testing locations for the FCAT Science test.

         changes have been made) report to former testing location from 3/10 and 3/11

         for an extended time. 

7. Monday(03/15): TEST on Ch.24. HW: Go to website to view notes

and links for Ch.25 - Reflection of Light.

Best to send an email to rpersin@fau.edu.

1. All objects above the temperature of absolute zero (-273.15° Celsius)

radiate energy to their surrounding environment. This energy, or radiation,

is emitted as electromagnetic waves that travel at the speed of light.

2. Many different types of radiation have been identified. Each of these types

is defined by its wavelength. The wavelength of electromagnetic radiation

can vary from being infinitely short to infinitely long.

3. Visible light is a form of electromagnetic radiation that can be perceived by

our eyes. Light has a wavelength of between 0.40 to 0.71 micrometers (µm).

4. Solar radiation spans a spectrum from approximately 0.1 to 4.0 µm.

The band from 0.1 to 0.4 micrometers is called ultraviolet radiation.

5. About 7% of the sun's emission is in this wavelength band. About 48% of

the sun's radiation falls in the region between 0.71 to 4.0 micrometers.

6. This band is called the near (0.71 to 1.5 micrometers) and far infrared

(1.5 to 4.0 micrometers).

7. Light is not the only example of an electromagnetic wave. Other

electromagnetic waves include the microwaves you use to heat up food for

dinner, the radio waves that are broadcast from radio stations, ultra-

violet radiation that kills germs, X-Rays used to "see" broken bones, and

gamma radiation that helps to cure cancer patients.

8. To examine the properties of the electromagnetic waves, let’s consider for

simplicity an electromagnetic wave propagating with velocity v in the +x

direction, with the electric field E pointing in the +y direction and the

magnetic field B in the +z direction.

9. We've already learned how moving charges (currents) produce magnetic

fields. A constant current produces a constant magnetic field, while a changing

current produces a changing field.

10. We can go the other way, and use a magnetic field to produce a current, as

long as the magnetic field is changing. This is what induced Emf was all about.

A steadily-changing magnetic field can induce a constant voltage, while an

oscillating magnetic field can induce an oscillating voltage.

11. Those two points are key to understanding electromagnetic waves:

(a) an oscillating electric field generates an oscillating magnetic field, and

(b) an oscillating magnetic field generates an oscillating electric field.

12. An electromagnetic wave (such as a radio wave) propagates outwards from

the source (an antenna, perhaps) at the speed of light. What this means in

practice is that the source has created oscillating electric and magnetic fields,

perpendicular to each other, that travel away from the source.

13. The E and B fields, along with being perpendicular to each other, are

perpendicular to the direction the wave travels, meaning an electromagnetic

wave is a transverse wave.

14. Basically, an electromagnetic wave can be created by accelerating charges;

moving charges back and forth will produce oscillating electric and magnetic

fields, and these travel at the speed of light.

15. It would really be more accurate to call the speed of light "the speed of

an electromagnetic wave", because light is just one example of waves of

this type.

16. The speed of light in vacuum is given by  c = 3.00 x 10⁸ m/s . As we'll go

into later in the course when we get to relativity, c is the ultimate speed limit

in the universe. Nothing can travel faster than light in a vacuum.

17. There have been many documented attempts to measure the speed of

visible light. All were based on the fact that light travels in straight lines away

from the source, and d = v∙Δt. We will discuss these attempts in class when

we talk about the work of Galileo (1564-1642), Olaus Roemer (1644-1710),

Jean Foucault (1819-1868), and Albert Michelson 1852-1931).

18. Meanwhile, all this was going on in the midst of the 200 year debate

about what type of phenomenon light was. Wave or particle? The particle

theorists were Isaac Newton (1642-1727), later followed notably by the French

mathematician Pierre Simon LaPlace (1789-1827). Robert Hooke (1635-1703)

and Christian Huygens (1629-1695) were of the inclination that light was waves.

19. A major triumph for the wave theorists occurred in 1802 when the British

physician and experimenter Thomas Young (1773-1829) was able to measure

the wavelength of light, λ . He did this by diffracting light through two tiny

openings and deriving the wavelength from the interference pattern on a screen.

20. Theoretically, there is a wonderful connection between c, the speed of light

in a vacuum, and the constants that appeared in the electricity and magnetism

equations, the permittivity of free space and the permeability of free space.

21. The great Scottish Physicist, James Clerk Maxwell (1831-1879), who showed

that all of electricity and magnetism could be expressed by four basic equations,

also worked out that the speed of light is c = 1/√(ε_oμ_o) . Recall that  

ε_o = 8.85x10^-12 C²/Nm² and μ_o = 4π x 10^-7 Tm/A. This clearly shows the link

between optics, electricity, and magnetism. (Unification, anyone?)

22. Something interesting about light, and electromagnetic waves in general, is

that no medium is required for the wave to travel through. Other waves, such

as sound waves, can not travel through a vacuum. An electromagnetic wave is

perfectly happy to do that.

23. An electromagnetic wave, although it carries no mass, does carry energy.

It also has momentum, and can exert pressure (known as radiation pressure).

The reason tails of comets point away from the Sun is the radiation pressure

exerted on the tail by the light (and other forms of radiation) from the Sun.

24. The energy carried by an electromagnetic wave is proportional to the

frequency of the wave. The wavelength and frequency of the wave are

connected via the speed of light. This produces the wave equation for

light which is c = fλ , velocity = frequency x wavelength.

25.Electromagnetic waves are split into different categories based on their

frequency (or, equivalently, on their wavelength). In other words, we split up

the electromagnetic spectrum based on frequency.

26. Visible light, for example, ranges from violet to red. Violet light has a

wavelength of 400 nm, and a frequency of 7.5 x 10¹⁴ Hz. Red light has a

wavelength of 700 nm, and a frequency of 4.3 x 10¹⁴ Hz.

27. Any electromagnetic wave with a frequency (or wavelength) between

those extremes can be seen by humans. Visible light makes up a very small

part of the full electromagnetic spectrum.

28. Electromagnetic waves that are of higher energy than visible light (higher

frequency, shorter wavelength) include ultraviolet light, X-rays, and gamma

rays. Lower energy waves (lower frequency, longer wavelength) include

infrared light, microwaves, and radio and television waves.

29. The energy in an electromagnetic wave is tied up in the electric and

magnetic fields. In general, the energy per unit volume in an electric field is

given by: u = ½ε_oE² .

30. In a magnetic field, the energy per unit volume is: u = ½B²/μ_o.

31. An electromagnetic wave has both electric and magnetic fields, so the

total energy density associated with an electromagnetic wave is:

u = ½ε_oE² + ½B²/μ_o.

32. It turns out that for an electromagnetic wave, the energy associated with

the electric field is equal to the energy associated with the magnetic field, so

the total energy density can be written in terms of just one or the other:

u = ε_oE²  or u =B²/μ_o.

33. It can also be shown that for an electromagnetic wave moving through a

vacuum, E = cB.

34. A more common way to handle the energy is to look at how much energy

is carried by the wave from one place to another. A good measure of this is

the intensity of the wave, which is the power that that the wave carries

perpendicular through a surface divided by the area of the surface.

35. The intensity, S, and the energy density, u, are related by a factor of c,

therefore, S = cu = ½cε_oE² + ½cB²/μ_o = cε_oE² = cB²/μ_{o .}

36. Generally, it's most useful to use the average power, or average intensity

of the wave. To find the average values, you have to use some average for

the electric field E and the magnetic field B.

37. Appealing to the mathematics of Statistics, the root mean square, rms,

averages are used. The relationship between the peak and rms values is:

E_rms = (1/√2)E_o   and   B_rms = (1/√2)B_o  .

38. The Doppler Effect, named after Christian Doppler (1803-1853), from

Austria, is the change in frequency and wavelength of a wave that is

perceived by an observer moving relative to the source of the waves.

39. For waves which do not require a medium, such as light, only the

relative difference in velocity between the observer and the source needs

to be considered, f_o = f_s(1 ± v_rel/c) . We will discuss the implications of this

equation in class.

39. Under certain conditions it is possible for all the vibrations in a light

beam to be confined to one plane at right angles to the beam. Such a beam

is said to be polarized. The French physicist E. L. Malus (1775-1812)

discovered this property of light.

40. When two pieces of polarizing material are used, one after the other,

the first is called the polarizer and the second, the analyzer. If the average

intensity of polarized light falling on the analyzer is S_o , the average

intensity of light leaving the analyzer, S, is given by Malus' Law, which is

S = S_ocos²(θ) , where is the angle between the transmission axes of the

polarizer and analyzer.

41. And still, we need these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct equation to use

(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown

(v) substitute-in the given information and simplify.