From: Ronald Wong (ronwong@inreach.com)
Date: Mon Oct 23 2000 - 23:34:09 PDT
Message-Id: <l03102800b619916d1fb3@[209.209.18.42]> Date: Tue, 24 Oct 2000 00:34:09 -0600 From: Ronald Wong <ronwong@inreach.com> Subject: light's frequency and black holes
David Lauter's students came up with some very nice questions:
>"How is it possible to determine the frequency or the wavelength of light?
>(I know you must use Planck's constant, so I suppose a good answer would be
>to explain how Planck figured out his constant. )"
Traditionally, the frequency of light is determined indirectly. You
determine it's wavelength and then divide it into the value for the speed
of light.
So, to answer the obvious, we must answer their question: "How is it
possible to determine...the wavelength of light?"
Interference is the magic word here.
For most students, it's best understood after they have studied wave motion.
Nothing beats a series of activities involving a ripple tank for getting
the message across clearly (if you don't have a class set of ripple tanks,
a demo with one will do). With the ripple tanks, the students can clearly
see that although waves have a number of properties similar to that of
particles, they have two, very strange properties that set them apart:
diffraction and interference.
Okay, so you don't have ripple tanks or didn't cover wave properties. Try
at least a little background story to set them up for your demo of
diffraction and interference and the measurement of the wavelength of light.
The story: Quite recently - relative to the thousands of years of recorded
history - those who should know about such matters thought that light
traveled in straight lines. Newton was one such fellow and it went along
with his idea that light was a stream of particles. There is ample evidence
of this all around us and you should give your students examples from their
everyday experiences. You might even demonstrate a few for them (sharp
shadows, pinhole images, etc.).
Having established that common sense seems to indicate that light travels
in straight lines, you then whip out your showcase lamp and set it up in
front of the class (preferable with the filament vertical). Turn it on and
have them draw a sketch of what the luminous filament looks like (the
entire demo is done with the students seated at their desks by the way).
Hopefully, they'll all draw a thin vertical line.
Then have them form a "V" with their index and middle finger and place it
against their eye with the filament framed between them. Tell them to
slowly bring their fingers together until they almost touch while still
keeping the filament in view. At some point a few of your students will
say, "wow". Have them draw what it is that they see (some kids will say,
"wow" just because others said, "wow"). They'll have noticed that at some
point the thin filament became fatter as the fingers came together. If they
are really observant (and most of them are), they'll notice a series of
bright bands left and right of the "fattened" filament.
If they haven't studied the property of waves, then you'll have to point
out to them that two things have been demonstrated here: A) That light
spreads out as it passes through very small openings and B) That light
interferes with itself (producing the dark and bright regions).
In other words, they have made the important discovery that light has the
properties of a wave. It can bend around the edges of obstacles into the
shadow region (i.e. diffracts) and it can interfere with itself. In other
words, light is a wave phenomena - no matter what textbooks and established
scholars have said.
For those students who can't seem to "get it" with their own two fingers,
suggest to them the use of two pencils or pens. They'll get perfect images
of the phenomena (it's cooler to create it with a pair of fingers though).
Now comes the important step: Have them squeeze their fingers/pencils/pens
a little closer to one another and note the change in the pattern that
they've been looking at. They'll notice two things: A) the pattern spreads
out more - confirming that it is indeed diffraction - and yielding better
resolution in the process and B) because of the greater resolution, they
can now begin to see color in the bands on the left and right of the
central, fuzzy filament. It is at this point that you can ask them which
color is diffracted the most and which the least. With the classroom lights
on or in a room with no blackout shades, they'll probably say red the most
and green the least. With blackout shades and a darkened room they'll be
able to see that blue is diffracted the least.
If you've covered wave properties, they'll know that this is evidence of
the fact that red has a greater wavelength than blue and that the
wavelength can be found by knowing the size of the opening and the position
of the respective colors in their field of view. Shows what you can do
with a little preparation, two fingers and a showcase lamp.
If you haven't, then.....
At this point, I hand out the diffraction gratings where the "openings" are
so small that they can only see the first (and maybe second) order
interference pattern - They usually go bananas over the "purity" of the
colors that they can see and start checking out all the light sources they
can get their hands on; I have them calibrate their gratings (I happen to
have had a sodium vapor lamp in my lab for this purpose); and then I have
them get the wavelength and frequencies of the various colors of light
using just a pair of meter sticks and their calibrated diffraction
gratings.
The first thing they learn is that the manufacturer's claim for the
diffraction constant is occasionally way off the mark (another example of
the fallibility of "authority"). The second thing they learn is that they
can get excellent results with their very simple tools.
I guess what I'm saying, David, is that it wouldn't take much for your
students to answer their own question - coming up with the actual
wavelengths of light by themselves in the process.
>"If all light in empty space travels at the same speed what happens when
>light falls into a black hole? Doesn't it go faster and faster?"
In his Theory of Relativity, Einstein claimed that the speed of light was
independent of the frame of reference it was traveling in. No matter what
frame of reference you are in, when you measure the speed of light, you
come up with the SAME number. This is true whether you are outside the
black hole, inside the black hole, or traveling from one to the other. The
speed of light is everywhere the same. It will never be found going faster
or slower.
This is a VERY strange idea if you think about it. But so far every test of
his theory of both general and special relativity has confirmed them and
their underlying claim that the speed of light is independent of the frame
of reference of the observer .
>And finally,"But the light can't come out of a black hole so it must stop.
The black hole has three regions associated with it.
1. At it's center sits the miniscule singularity.
2. Around the singularity is a region called the event horizon. The radius
of the event horizon is a function of the mass of the star that has
collapsed to form the black hole (the simple formula for it can be derived
by any high school student familiar with the concept of escape velocity).
3. Surrounding the event horizon is a larger sphere called the photon sphere.
(its radius is 3/2 that of the event horizon if I remember correctly)
What light can't "come out of" is the photon sphere associated with the
black hole when the source of the light drops below the event horizon. If
the light source is between the photon sphere and the event horizon,
information/light can still find it's way out into the rest of the universe
- if it is traveling in the right direction. Once the light source drops
below the event horizon, only a detector between the photon sphere and the
event horizon will "see" this light and, again, only if the light is
traveling in the right direction and the detector near the event horizon.
The light doesn't stop. It's path simply becomes so curved by the great
curvature of space time inside the black hole that it's path is bent back
away from the photon sphere even when it is directed towards it.
>Does light stop in a black hole?"
Excellent question. Light "stops" when it's absorbed by something. This
could be an object that has passed through the photon sphere/event horizon
and is falling deeper into the black hole or it could be the massive star
that has collapsed into what is known as the singularity. The latter case
involves a region where there is claimed to be infinite density and
infinite curvature of space-time. Since the physics of this region of the
black hole is up for grabs presently, what light will do once it gets there
is anybody's guess.
You must be doing some interesting things with your students to have them
come up with such entertaining questions David. I can't believe that you
aren't having a good time as well.
Cheers - ron
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