Friday, Feb. 22, 2019

Marcus Roberts "Bolivar Blues" (3:15), music from the Preservation Hall Jazz Band "El Manicero" (9:03) featuring Cuban jazz pianist Ernan Lopez Nussa, Coldplay and Buena Vista Social Club "Clocks" (4:59).   If you have some extra time you really should watch this 60 Minutes segment about Marcus Roberts "the greatest American musician most people have never heard of."

 We'll use page 61, page 62, page 63, page 64, page 65, and page 66 from the ClassNotes today.

An In-class Optional Assignment was handed out in class today.  If you weren't in class you can download the assignment and turn it in at the start of class next Monday and receive at least partial credit.
We'll quickly review a couple of figures because I didn't do a very good job of explaining them in class on Wednesday.

2 ways of describing or differentiating between different types of EM radiation: wavelength & frequency


You can describe the radiation spatially using the wavelength.  In this case you're looking at the EM radiation at different locations at one particular time.

Or you can describe the EM radiation temporally using the frequency.  Frequency is the number of up and down cycles a charge would complete per second. 

The following figure illustrates how energy can be transported from one place to another (even through empty space) in the form of electromagnetic (EM) radiation.




You add energy when you cause an electrical charge to move up and down and create the EM radiation (top left).

In the middle figure, the EM radiation that is produced then travels out to the right (it could be through empty space or through something like the atmosphere). 

Once the EM radiation encounters an electrical charge at another location (bottom right), the energy reappears as the radiation causes the charge to move.  Energy has been transported from left to right.

Wavelength, frequency, and energy
There's an important association between wavelength, frequency, and the energy in EM radiation.




 EM radiation can be created when you cause a charge to move up and down. If you move a charge up and down slowly (upper left in the figure above) you would produce long wavelength radiation that would propagate out to the right at the speed of light.  If you move the charge up and down more rapidly you produce short wavelength radiation that propagates at the same speed.

Once the EM radiation encounters the charges at the right side of the figure above the EM radiation causes those charges to oscillate up and down.  In the case of the long wavelength radiation the charge at right oscillates slowly.  This is low frequency and low energy motion.  The short wavelength causes the charge at right to oscillate more rapidly - high frequency and high energy.

These three characteristics: long wavelength / low frequency / low energy go together. So do short wavelength / high frequency / high energy.  Note that the two different types of radiation both propagate at the same speed.




The electromagnetic spectrum
The EM spectrum is just a list of the different kinds of EM radiation.  A partial list is shown below.





In the top list, shortwave wavelength/high energy forms of EM radiation are on the left (gamma rays and X-rays for example).  Microwaves and radiowaves are longer wavelength/lower energy forms of EM radiation.

We will mostly be concerned with just ultraviolet light (UV), visible light (VIS), and infrared light (IR).  These are shown on an expanded scale below.  Note the micrometer (millionths of a meter) units used for wavelength for these kinds of light.  The visible portion of the spectrum falls between 0.4 and 0.7 micrometers.   UV and IR light are both invisible.  All of the vivid colors shown above are just EM radiation with slightly different wavelengths.  When you see all of these colors mixed together, you see white light.

I've tried to demonstrate colors mixing together to make white light using laser pointers.



But it's too hard to get them adjusted so that the small spots of colored light all fall on top of each other on the screen at the front of the room.  And even if you do the small spot of light is so small that it's hard to see clearly in a large classroom (you need to do the experiment on a piece of paper a few feet away).

Here's the basic idea, you mix red green and blue light together.  You see white light were the three colors overlap and mix in the center of the picture above.  Doesn't it seem odd that green and red mix to produce yellow?


Rules governing the emission of EM radiation
We'll spend a big part of the class learning about and trying to understand a couple of rules governing the emission of electromagnetic radiation.  Here they are:

1.
Everything warmer than 0 K will emit EM radiation.  Everything in the classroom: the people, the furniture, the walls and the floor, even the air, are emitting EM radiation.  Often this radiation will be invisible so that we can't see it and weak enough that we can't feel it (or perhaps because it is always there we've grown accustomed to it and ignore it).  Both the amount and kind (wavelength) of the emitted radiation depend on the object's temperature.  In the classroom most everything has a temperature of around 300 K and we will see that means everything is emitting far-infrared (FIR) radiation with a wavelength of about 10µm.

2.
The second rule allows you to determine the amount of EM radiation (radiant energy) an object will emit.  Don't worry about the units (though they're given in the figure below), you can think of this as amount, or rate, or intensity.  Don't worry about σ (the Greek character rho) either, it is just a constant.  The amount depends on temperature to the fourth power.  If the temperature of an object doubles the amount of energy emitted will increase by a factor of 2 to the 4th power (that's 2 x 2 x 2 x 2 = 16).  A hot object just doesn't emit a little more energy than a cold object it emits a lot more energy than a cold object.  This is illustrated in the following figure (found on page 64 in the ClassNotes):



The cool object is emitting 2 arrows worth of energy.  This could be the earth at 300 K.  The warmer object is 2 times warmer, the earth heated to 600 K.  The earth then would emit 32 arrows (16 times more energy).

The earth has a temperature of 300 K.  The sun is 20 times hotter (6000 K).  Every square foot of the sun's surface will emit 204 (160,000) times more energy per second than a square foot of the earth's surface.

3.
The third rule tells you something about the kind of radiation emitted by an object.  We will see that objects usually emit radiation at many different wavelengths but not in equal amounts.  Objects emit more of one particular wavelength than any of the others.  This is called  λmax ("lambda max", lambda is the Greek character used to represent wavelength) and is the wavelength of maximum emission.  The third rule allows you to calculate  λmax. The tendency for warm objects to emit radiation at shorter wavelengths is shown below.



The cool object could be emitting infrared light (that would be the case for the earth at 300 K).  It might be emitting a little bit of red light that we could see.  That's the 2 arrows of energy that are colored red.  The warmer object will also emit IR light but also shorter wavelengths such as yellow, green, blue, and violet (maybe even some UV if it's hot enough).   Remember though when you start mixing different colors of visible light you get something that starts to look white.  The cool object might appear to glow red, the hotter object would be much brighter and would appear white.

Here's another way of understanding Stefan Boltzmann's law and Wien's Law (the graph below is on the bottom of page 63 in the ClassNotes).

1.
Notice first that both and warm and the cold objects emit radiation over a range of wavelengths (the curves above are like quiz scores, not everyone gets the same score, there is a distribution of grades).  The warm object emits all the wavelengths the cooler object does plus lots of additional shorter wavelengths.

2.
The peak of each curve is λmax  the wavelength of peak emission (the object emits more of that particular wavelength than any other wavelength).  Note that λmax has shifted toward shorter wavelengths for the warmer object.  That is Wien's law in action.  The warmer object is emitting lots of types of short wavelength radiation that the colder object doesn't emit.

3.
The area under the curve is the total radiant energy emitted by the object.  The area under the warm object curve is much bigger than the area under the cold object curve.    This illustrates the fact that the warmer object emits a lot more radiant energy than the colder object.


It is relatively easy to see Stefan-Boltzmann's law and Wien's Law in action.  The class demonstration consisted of an "ordinary" 200 W tungsten bulb is connected to a dimmer switch (see p. 65 in the photocopied ClassNotes and note that setting 0 is not included in the figure in the ClassNotes).  We'll be looking at the EM radiation emitted by the bulb filament. 




The graph at the bottom of p. 65 has been split up into 3 parts and redrawn for improved clarity.










We start with the bulb turned off (Setting 0).  The filament will be at room temperature which we will assume is around 300 K (remember that is a reasonable and easy to remember value for the average temperature of the earth's surface).  The bulb will be emitting radiation, it's shown on the top graph above.  The radiation is very weak so we can't feel it.  We can use Wien's Law to calculate the wavelength of peak emission,  λmax .  The wavelength of peak emission is 10 micrometers which is long wavelength, far IR radiation so we can't see it. 

Next we use the dimmer switch to just barely turn the bulb on (the temperature of the filament is now about 900 K).  The bulb wasn't very bright at all and had an orange color.  This is curve 1, the middle figure.  Note the far left end of the emission curve has moved left of the 0.7 micrometer mark - into the visible portion of the spectrum.  That is what you were able to see, just the small fraction of the radiation emitted by the bulb that is visible light (but just long wavelength red and orange light).  The Draper point is the approximate temperature above which almost all solid materials begin to visibly glow (798 K , 525˚ C , 977˚ F see https://www.quora.com/At-what-temperature-do-all-objects-start-emitting-visible-light). 

Most of the radiation emitted by the bulb at setting 1 is to the right of the 0.7 micrometer mark and is invisible IR radiation (it is strong enough now that you could feel it if you put your hand next to the bulb).

Finally we turn on the bulb completely (it is a 200 Watt bulb so it got pretty bright).  The filament temperature is now about 3000K.  The bulb is emitting a lot more visible light, all the colors, though not all in equal amounts.  The mixture of the colors produces a "warm white" light.  It is warm because it is a mixture that contains a lot more red, orange, and yellow than blue, green, and violet light.  It is interesting that most of the radiation emitted by the bulb is still in the IR portion of the spectrum (lambda max is 1 micrometer).  This is invisible light.  A tungsten bulb like this is not especially efficient, at least not as a source of visible light.





This is a picture of Pahoehoe lava.  The molten rock is hot enough to be emitting visible light.  If fact the color can be used to estimate the temperature of the lava, yellow indicates a temperature of about 1000 to 1200 °C (1,830 to 2,190 °F). (source of this photograph: https://en.wikipedia.org/wiki/Black-body_radiation, a good article on blackbody radiation that contains a figure showing the color you would see from objects of different temperatures)


Light emitted by the earth and sun; warm and cool white; tungsten bulbs, compact fluorescent bulbs, and LED bulbs

The figure compares the light emitted by the sun and the earth.



The curve on the left is for the sun.  The surface of the sun has a temperature of 6000 K so we can use Wien's law to calculate λmax .  It turns out to be 0.5 micrometers.  This is green light; the sun emits more green light than any other kind of light.  The sun doesn't appear green because it is also emitting lesser amounts of violet, blue, yellow, orange, and red - together this mix of colors appears white (it's a cooler white than emitted by a tungsten bulb).  44% of the radiation emitted by the sun is visible light,  Very nearly half of sunlight (49%) is IR light (37% near IR + 12% far IR).  7% of sunlight is ultraviolet light.  More than half of the light emitted by the sun (the IR and UV light) is invisible.

100% of the light emitted by the earth (temperature = 300 K) is invisible far IR light.  The wavelength of peak emission for the earth is 10 micrometers. 

Because the sun (surface of the sun) is 20 times hotter than the earth the sun's surface emits energy at a much higher rate than the earth (160,000 times higher).  Note the vertical scale on the earth curve is different than on the sun graph.  If both the earth and sun were plotted with the same vertical scale, the earth curve would be much too small to be seen.


Ordinary tungsten bulbs (incandescent bulbs) produce a lot of wasted energy.  This is because they emit a lot of invisible infrared light that doesn't light up a room (it will warm up a room but there are better ways of doing that).  The light that they do produce is a warm white color (tungsten bulbs emit lots of orange, red, and yellow light and not much blue, green or violet). 

Energy efficient compact fluorescent lamps (CFLs) are being touted as an ecological alternative to tungsten bulbs because they use substantially less electricity, don't emit a  lot of wasted infrared light, and are supposed to last longer.  CFLs come with different color temperature ratings.  What that is really referring to is the mix of different colors that they use to produce white light.

The bulb with the hottest temperature rating (5500 K ) in the figure above is meant to mimic or simulate sunlight (daylight).  The temperature of the sun is 6000 K and lambda max is 0.5 micrometers.  The spectrum of the 5500 K bulb is similar.  Even though the color temperature is high this is referred to as cool white because it contains more blue, green, and violet light.

The tungsten bulb (3000 K) and the CFLs with temperature ratings of 3500 K and 2700 K produce a warmer white. 

Three CFLs with the temperature ratings above were set up in class so that you actually could see the difference between warm and cool white light.  Personally I find the 2700 K bulb "too warm," it makes a room seem gloomy and depressing (a student in class once said the light resembles Tucson at night).   The 5500 K bulb is "too cool" and creates a stark sterile atmosphere like you might see in a hospital corridor.  I prefer the 3500 K bulb in the middle.

The photograph below (from this source) showing the difference between warm white and cooler white is one of the best I've seen. 



The bulb on the far right has a tungsten filament and a color temperature of 3000K.  Then moving from left to right are CFL bulbs with color temperatures of 6500 K, 5500 K, 4100 K, 3500 K, and 2700 K.

There is one downside to these energy efficient CFLs.  The bulbs shouldn't just be discarded in your ordinary household trash because they contain mercury.  They should be disposed of properly (at a hazardous materials collection site or perhaps at the store where they were purchased).  I suspect a lot of people don't do that.

It probably won't be long before LED bulbs begin to replace tungsten and CFL bulbs.  The price has dropped dramatically in the last year.

LED stands for light emitting diode.  We won't be looking at them in detail except to say that a single LED can produce only a single color, it can't produce white light. 


What is done instead is to put three small LEDS, producing red, green and blue light, in close proximity.  When they are illuminated the three colors mix together to produce white light like in an earlier figure in today's notes (reproduced above with some additional comments, see also "RGB color model" in Wikipedia  ).  By varying the intensity of the individual LEDs you can produce a wide variety of colors.  CFLs sometimes take 30 seconds or a minute to come to full brightness.  LED bulbs turn on instantaneously.  Another important advantage is that LED bulbs do not contain mercury.

Just as with CFLs you can buy LED bulbs with different color temperatures, i.e. bulbs that produce warm white light that resembles what is produced by a tungsten bulb and bulbs that produce a cooler white that is more similar to sunlight.  You'll often see the bulbs grouped as soft white (warm white), bright white, and daylight.  I'll show some examples in class.