# "LET THERE BE ELECTROMAGNETIC RADIATION"

### Light can be thought of as a WAVE...

= wavelength = distance between crests (or any two identical spots). The units are distance units like feet or meters.

f or = frequency = Number of times a boat goes up and down per unit time. The units are 1/(time), e.g. 1/second. Sometimes this is stated as cycles/second or Hertz (Hz).

v = speed of the wave. Units of distances/time.

The boat goes up and down with the waves. What about the water?

Q. Just what is traveling in the direction of the waves?

Energy and information. Waves are a disturbance traveling through a medium (although E-M radiation can travel in a vacuum).

There are other kinds of waves (ocean waves are sometimes called "gravity waves" or "surface waves")

• Sound Waves are density/pressure waves.

• The speed of sound in air (on a cool day) is ~1000 feet/second (this is the basis of the old "distance of the thunderstorm" trick). Do the air molecules travel at this speed? In a higher-density medium (for example, railway tracks) a sound wave travels faster.

### So, what does this have to do with LIGHT?

• An electrically charged particle has an electric field extending to infinity. If this charge is accelerated , the position of the field center changes and that information propogates out as a "kink" in the field lines. A magnetic field is also induced at the kink. This traveling kink is an electro-magnetic wave.
• The SPEED with which the information that the charge accelerated travels outward is called the Speed of Light.

Q. What is the speed of light in miles/hour?

 c = 3 x 105 km x 0.62 miles = 186,000 miles/sec. sec 1 km

 186,000 miles x 60 sec x 60 min = 6.7 x 108 miles/hr. sec 1 min 1 hour

Q. The Sun is 93,000,000 miles away. How long does it take for the light that leaves the Sun to reach the Earth?

 Time = 9.3 x 107 miles = 500 sec x 1 min = 8.3 minutes. 186,000 miles/sec 60 sec

Q. What is a Light Year?

First, this is a unit of DISTANCE (not time). It is the distance light travels (in a vacuum) in 1 year.

Light travels:

 186,000 miles x 60 sec x ... sec 1 min

= 5.86 x 1012 miles/year (!)

Lookback Times: The disk of our Galaxy has a diameter of around 50,000 LY. The nearest big galaxy (Andromeda) is 2 million light years distant. So we see Andromeda as it looked 2 million years ago.

The most distant objects we have observed in astronomy have "look-back" times of over 8 billion years. The finite speed of light is very handy in that it allows us to look back in time...

## More on Waves

There are only a few properties of light...

• Frequency

• Wavelength

• Speed

For light in a given medium (for example the vacuum of space), the speed is constant so Frequency and Wavelength are essentially different ways of describing the same thing.

 c = f x f = c

Frequency (f) and wavelength are inversely proportional to one another - as one goes up, the other goes down to keep their product constant.

• Amplitude

• Energy

The energy of an E-M wave depends on the amplitude and the wavelength. For a given amplitude, shorter (higher f) waves carry more energy.

There is an alternative description for E-M radiation in which the light energy is carried in Photons (like little bullets of light) that have associated energy, wavelength and frequency. We will use these descriptions interchangably.