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Journal
Thursday, September 29, 2005
Rule about the paper:
- 20 pg limit starting from introduction
- no mention of name, high school, gender, reseach institutions
- Abstract - word limit 100-200
From collegeboard.com
1. Purpose of the Research
problem to be solved
research question to be answered
hypotheses to be tested
2. Rationale for the Research
Why is the work significant?
3. Pertinent scientific literature
provide a brief review of most relevant literature
cite all relevant literature
4. Prior work and contributions of other on this project
info. on concurrent similar or related work/project in the laboratory
5. Methodology
Describe the methods used to allow someone trained in the field to understand
What was done
How it was accomplished
6. Results
result of research
7. Discussion
How result addresses the problem to be solved or research
question to be addressed
Discuss any interpretations that can be drawn from the results
8. Conclusion
What questions still need to be answered?
Does the Research report have a basis for future work?
Audience: Research scientists in academic and governmental laboratory
settings
1. Assemble
- Confirmation page
- Title page
- Abstract
- Research Report
2. *Staple left hand corner
3. Original plus 3 photocopyed mentor form
4. Mail 4 sets of paper (in color)
5. Make 3 copies of confirmation page
Some thoughts about so-far Siemens paper after going through it few
times:
- Satisfied with the Jones Calculus section, except for a big space
under the table, and maybe the first sentence under polarized light
- Introduction, few weird wording or grammar
- Birefringence : nslow => n should be in math mode and slow not
- Expand Polage section!!!
- Polarized Light somehow too weak - why
- Too much redundance, don't describe methods in other sections, esp. results
- Better organization!! - esp. visual observations
- More on birefringence: cellulose, birefringent minerals, ex. of dichroic materials
- Be more precise and succinct
- Too much methods in results
Saturday, September 24, 2005
Siemen's Mailing Deadline: Friday, September 30
Dr. Noé, Nilus, and I have been working on our team project:
A Mathematical and Experimental Analysis of Color Patterns in
Polarized Light Art. This week I came to the lab Wednesday,
Thursday, Friday, and Saturday to work on my project. It was a
crazy week my school work is being neglected and my sleep pattern
if very bad. Anyway we got some hot graphs and calculations. We
used Dos and Mathematica to generate graphs. Dr.Noé spent
about six hours generating these pretty sets of curves. One things
for sure is that through these few days, we started understanding
what actually happened in two polarizers and cellophane setup. Our
understanding expanded dramatically along with some data. Today
Dr.Noé and I spent some time working on the headings and
subheadings of my paper, plus just general organization. Actual
writing is what needs to be done, but through today's achievement,
we got the general idea and also few graphs and calculations. I
need to go do the writing now but once Siemens is over I can write
more journal entries.
Monday, August 15, 2005
Important news: The RadioShack guy overcharged me plus gave me few
wrong things. I spent approximately 140 dollars at RadioShack! I'm
broke now!
I built a Simple LED Flasher by myself today! I went to the
RadioShack, because I decided to build a circuit for my friend's
birthday that is coming up.
Details: So I bought the Forest M. Mims III electronics kit as a
reference. Then I bought an IC breadboard socket, photocells, a
5kΩ potentiometer, a hook-up wire (contains three colored
wires: green, red, and black), an adjustable voltage regulator, and
four 9V batteries. Then I bought my favorite things, the LEDs: red,
white, infrared, blue, and bicolor. The LEDs are all 5 mm and all
of them have different intensities. First I built a Simple LED
Flasher using the kit. Then by using the circuit diagram in the
book and kind of peeking at the built circuit, I built the same
thing on the breadboard. Now I am going to try to build a
Dark-Activated Dual LED Flasher, which Nilus and I built at
the lab. Hopefully, I'll finish it soon, because I need to finish
packing. I am leaving for Korea late tonight. I also walked to the
post office today and sent 6 burned CDs for the lab! I took it to
the post office like 2 minutes before it closed. Post officer(?)
said that the CDs will arrive by tomorrow.
I am at the airport now!!! I have about 2 hours and 20 more minutes
untill the airplane leaves. It is 11:03pm right now. I probably
should be spending this time doing my HW.
About me: Anyway, I think that sometimes you can say you know
something well when you can write about it really well: when you
can make a person who knows nothing about that topic understand
from what you wrote (even if it is a little bit). When you've read
about it from many different sources, have discussed/debated it
with somebody else, and if you actually understand it enough to
grasp it, when you write about it, it'll just come out fast from
your mind, in your own words. To me, writing about "somethings" is
what I really love to do, although I am not a writer. I cannot
write a short story or piece of literature. Poems I can semi-do,
but it takes a long time. You can say that I have a bad
imagination, unless my opinion and argument count as my
imagination. To think about it now, I can only write about things
that already exist in my world/mind. This doesn't mean that I can't
write about other side of point of view. In other words, I just
can't create a new world, new people, and new lives. I can never
write and create at the same time. But when it comes to writing
about what I know very well, or at least thing I think I know very
well, I really enjoy it. I like writing about topics related to
polarized light, just on things I understand to some degrees. I
like writing about general topics in life, something that I can
freely talk about. I also like writing about myself, and things
related to me, as I am doing right now. To conclude, writing about
whatever you want to write about is very fun thing to do, something
you can really enjoy even if you know nobody is going to read
it. So what makes writing so special? I think that writing often
permits you to think and use what you know. In my belief, that is
what is beautiful about writing.
Friday, August 12, 2005
*Sunday, August 14: Backdating*
-- This journal entry is twelve-twentyfifth science related, or is it not --
Today is the last official day of Simons program. Thus, we
got kicked out of our dorm today. At the Laser Center, we had a
semi-party and a laser show with classical music. People organized
the setup for the laser show. The setup: laser was shot into the
small mirror attached to a speaker; speaker was attached to the
portable stereo. How it worked: the reflection of the beam was
projected on the ceiling; the vibration of the speaker resulted
from the loud and amplified sound waves; the vibration of the
speaker caused the vibration of the mirror; the laser beam on the
ceiling made various ramdom shapes, including stretched and twisted
oval shapes and somewhat expanded infinity symbols (polar
graphs?). One thing to note was that the shape was always a closed
one. In other words, line and curve were all connected without a
breakup. Music that were tried: Mendelssohn Violin Concerto,
Shostakovich Violin Concerto #1, Ave Maria (cello solo with
orchestra), Vivaldi: Four Seasons, etc. Later green and violet
lasers were also added, to make the show look "hotter." Liquid
Nitrogen (as always) in a Giant Container was also poured on
the floor today and it was evaporating all over the floor. Steam or
fog (whatever you call it) was everywhere on the floor. The carpets
froze, and it seemed like they were going to break.
Later we ordered pizzas. We ordered scillian, broccoli and garlic,
and eggplant. I never tried eggplant pizza before. Lindsey and Greg
suggested it, and it was so99999999999 good. Then we
went to Greg's room to get the speakers and DVDs to watch a
movie. As we were eating, we started watching "Death to Smoochy,"
which, in my opinion, was half comedy and half not. In a way, it
was a depressing movie, despite all the smoochy show, rhino custom,
and loving children, etc., because the main character in the movie
definitely got involved in the world he did not belong: corrupted
world of dirty power, force, and money. I didn't see the ending,
but I assume Smoochy dies, as inferred by the title of the movie. I
just hope he didn't become corrupted before he died.
Anyway, I was the first one to leave. To think about it now, it's
hard to believe that 7 weeks passed. Before, I thought 7 weeks will
be so long. But I made unforgettable memories and had a great fun
both at the lab and at the dorm. I value my experience here, but it
didn't end yet. I'll be back after I come back from Korea to do my
project.
So thanks to everyone for everything, or just most things,
excluding the wallet incidence, and sandal kidnapping case, and
much more (This is a joke). Things that comes to my mind: "hot"
political discussions, lunch at Jasmine, *making fun of few other
people*, taking Amol hostage when he was actually innocent both
times, liquid nitrogen, damped harmonic motion, euler's equation,
conference room, crews, Thai food, Indian food, free cookie,
vegetarianism, religion, President Bush, hanglider, CEO, classical
music, spark chamber, soccer, CJ interferometer, my "hot" website
(haha), my miscellaneous section, my mathematics courses,
electronics and LEDs, penguin and debian linux, visitors, German
words, pizza eating competition, .... and of course, FRIED ICE
CREAM, talking, and MATRIXIST.
Thursday, August 11, 2005
Why
we see only one color only when clean piece of cellophane is placed
in between two polaroids
Using
cellophane to convert a liquid crystal display screen into a three
dimensional display (3D laptop computer and 3D camera phone)
"Since the index of refraction of a material is in general a
function of the wavelength of the incident EM radiation (although
it is usually a very mild function of the wavelength), it is
possible for white light to enter a birefringent material and for
different colors to be seen at various positions and different
polarizations as the light emerges from the material. Cellophane is
a great example of this effect. Cellophane is birefringent as a
result of the process in which it is manufactured - a stretching
process makes the direction in the cellophane along the direction
of stretch physically different than the direction perpendicular to
the stretch. Placing a crumpled piece of cellophane between two
Polaroids shows a rainbow of colors emerging from the top Polaroid.
As the top Polaroid is rotated through 360° the various colors can
be seen to change to their complementary colors, and then back." Here
Wednesday, August 10, 2005
Thanks to Amol, now I have Debian GNU/Linux installed on my
desktop. So I can officially say I am a linux beginner!
"If we use white light in our demonstration, the cellophne sheet
will be of the proper half-wave thickness only for a particular
component of the white light, and the transmitted beam will have
the color of this component. The color transmitted depends on the
thickness of the cellophane sheet, and we can vary the effective
thickness of the cellophane by tilting it so that the light passes
through the cellophane at an angle, consequently through a longer
path in the cellophane. As the sheet is tilted the transmiltted
color changes." -- Richard Feynman, Feynman's Lectures: Volume
1
Scheisse(!): scha-i-sa = German word used to express anger or frustration; equivalent of "shit" or "crap"
Questions:
Derive mathematically - why half wave plate rotates the
polarization by 2θ for the angle difference of θ
Tuesday, August 9, 2005
I read more about the wave
plates. α =
2πd(ne-no)/λ is an equation for
the resulting phase difference after the linearly polarized light
has travelled through a birefringent matieral. Lowercase
α is the phase difference, d the thickness of a
waveplate, ne the index of refraction of an
extraordinary axis, no the index of refraction of
an ordinary axis, and λ the wavelength. Wave plates
are formed with "carefully adjusted thickness" of a birefringent
material (HyperPhysics).
As seen by the equation above, for a certain wavelength, thickness
of the waveplate determines the phase difference.
Malus's Law
Half wave plate = device such that, for θ, the
difference between the polarization of an incoming light and one of
the axes of the plate, polarization of the light is rotated by
2θ; converts left circularly polarized light into right
circularly polarized and vice versa; has a thickness that results
in a phase difference of 1/2 wavelength, or multiple of 1/2
wavelength.
Quarter wave plate = device that transforms a linearly
polarized light into a circularly polarized light and vice versa
Polaroid (Polarizer) = device that allows only one certain
polarization of light to go through - for a linearly polarized
light, if there is a component along that polarization, some light
will go through, but if there is no component along that
polarization, no light will go through - happens when the
polarization of the light is perpendicular to the polaroid's
orientation
Analyzer = device used to determine the polarization
direction of the light by seeing whether or not the light pass
through when the analyzer is at a given orientation; second
polarizer
We had two visitors from a German graduate school. Ruth was one of them. Anyway, they were very very nice.
Color Management (Gainsboro)
Monday, August 8, 2005
Today we had a brief discussion with where we were
going. Dr. No&eacutue; said that if I am leaving for Korea, I
should have a plan. So today, Nilus explained to me how Michelson
interferometer works. We talked about the possibility of using
the inferometer to measure the index of refraction of a
cellophane. Cellophane is a birefringent material. Birefringence,
referred to as "double refraction," is caused when atoms are bound
more tightly in one axis than in the other. A birefringent material
has two different indices of refraction, nslow and
nfast, for two different axes, x and y. Different
components of the E-field will go through different indices of
refraction. Thus, one component will travel faster than the other
component through the medium (v=c/n, lower the n, greater the
velocity and vice versa). Phase difference between the two
components results from (aforementioned) their different travel
speed through the medium. In effect, ellipically polarized light
will be produced. Circularly and linearly polarized light are just
special cases of elliptically polarized light. Circularly polarized
light is an elliptically polarized light with the same magnitude of
the components, out of phase by 90 degrees.
If you want to find the indices of refraction of the birefringent
material, first you need to find the axes of the material. Once you
find one axis, you know the other axis, because two axes are just
perpendicular. Then you send a linearly polarized light parallel to
one axis to find out the index of refraction. As of now, I don't
exactly what to use to find the index of refraction.
Goal:
To be productive.
To understand the wave plates better.
To observe the color effects of wave plates squeezed between two linear polarizers.
Learn:
λ/2 plate (half-wave plate)
λ/4 plate (quarter-wave plate)
Read:
Polarization in Elementary Wave Optics by Robert H. Webb.
Acomplishment:
λ/2 plate changes polarization
by 2θ for a θ, the angular difference between the optic
axes of the first polarizer and the cellophane. But this only
applies to certain wavelengths. I just made a simple observation
using two crossed polarizers with a λ/2 plate in
between. Refer to wave plate. Wave
plates result in the phase difference of the components of the
electric field, depending on the thickness of the birefringent
material for a specific wavelength. Wave plates are simply
birefringent material at a chosen thickness made to perform
specific tasks. Quarter-wave plates transform linearly polarized
light to circularly polarized light and vice versa. Quarter-wave
plates create λ/4 phase shift, and half-wave plates create
λ/2 phase shift.
Friday, August 5, 2005
Today was the REU presentation. I only stayed for several
presentations. One that particularly sparked my interest was
Design and Construction of a Spark Chamber by Michael Assis
and Eugene Vaynberg. First, they gave an amazing presentation. I
did not understand everything, but I was happy to understand some
things. They communicated with the audience very well. It wasn't a
powerpoint presentation. They brought their spark chamber and
described and demonstrated it.
Kyung, a Korean research student working under Professor Metcalf
visited today. He told me about lots of things that are related to
my project.
Thursday, August 4, 2005
"I think the driving force in physics is curiosity." --
Dr. Noé
"Mathematics is the queen of the sciences and number theory is the
queen of mathematics." -- Gauss
"God invented the integers; all else is the work of man." --
Kronecker
Agree or disagree with the above quotes.
We had the Simons Tour today. It happened to be really fun. People
were nice and interested in what we do. In the conference room, all
the high school students in the laser lab, which includes me, had
to introduce ourselves and briefly describe what our project is and
what we're doing. I got so nervous but it was a great
experience. Everybody, I hope this includes me, did a great job in
confidently and concisely explaining what he/she was interested in
doing and had done. After that, everybody came into our lab, and we
were at our stations to explain and show them what we are
doing. Because the 'second' one was informal, I could explain
things with more ease and more details. Some of the things I
explained:
Unpolarized light
Birefringent material vs. Quarter-wave plate : two axes, two
indices of refraction
Factors, which color/s of cellophane located between two linear
polarizers is dependent upon upon
Linear Polarizer
Monday, August 1, 2005
Dr. Noé showed the soldering iron and explained how it is
a feedback system:
Inside the soldering iron, there is a circuit that measures the
temperature of the soldering tip. When the temperature at the tip
is lower than that chosen by you, it turns on to heat up the
tip. When the temperature of the tip is higher, it turns off by
itself. The light turns on when it is heating up and turns off when
it is not. When two temperatures are very close, then the light
flashes. Possible reasons behind this can be that when the
temperatures are very close, the system becomes unstable, and maybe
the temperature of the tip is keep changing, being equal to the
chosen temperature momentarily and then changing a little, being
equal again, and on.In that case, the feedback system may not be
sure whether to turn off or turn on. The flashes were visible when
somebody blew on the tip, because the temperature of human breath
is less than 600°F (chosen temperature). Talking about fthe
eedback system, I just remembered Professor Metcalf's talk from the
other day. He said that when we take a shower, we become a feedback
system. We adjust the temperature of the water. If it's too hot we
lower it, and vice versa. Microprocessor also comes to my
mind. Mr. Schorn told me about the microprocessors.
If you know what a polarizer is probably you would have tried
fooling around with at least two linear polarizers before. Then you
know that when two linear polarizers are parallel, all the light
that comes through the first polarizer will go through the second
polarizer (ignoring the absorption by the gray of the
polarizer). Light around us, sunlight and light bulbs for example,
are unpolarized. There are different ways to visualize an
unpolarized light. One way is to think that unpolarized light has
no particular orientation or polarization. Using Greg's word, it's
just random. Other ways are: to think that its polarization
are in all directions, or that it has all polarizations; And to
think that light is unstable so that its polarization changes so
fast constantly. One way or the other, for unpolarized light all
the polarization effects cancel out. However, when an unpolarized
passes through the first linear polarizer, light will become
linearly polarized with the axis of polarization dependent upon the
θ of the polarizer.
Sunday, July 31, 2005
For fun, I started reading HTML tutorial
and CSS
tutorial to understand how they work and to learn from the
basics. So the first thing I learned is that HTML is an
acronym that stands for Hyper Text Markup
Language. CSS stands for Cascading
Style Sheets. I experimented with link
decorations.
Friday, July 29, 2005
In the morning, meaning 1-2 am, I learned about transpose matrices
and determinants.
Just a few things on matrices:
Matrix multiplication obeys the distributive law and the assoicative
law. As you will know from ordinary algebra, distributive law means
P(I+O) = PI+PO, just don't forget that now P represent a matrix P, I
represents, matrix I, and same for O. Associative law means that
any grouping in multiplication give the same result. Thus, HEAT =
H(EA)T = (HEA)T. However, matrix
multiplication is 'not commutative,' which means that the order
of the multiplications matter. Matrix product AB does not equal
BA. Transpose of a matrix is produced by interchanging the matrix's
rows and columns. One thing to know about the transpose and its
orignial matrix: "The transpose of the product of two matrices
is the product of their transpose in reversed order." Which
means: (YO)T = OTYT. Using that
and the assoicative law for matrix multiplication, you can prove
(ABCDEF)T =
FTETDTCTBTAT. For
example, (PIE)T = [(PI)E]T =
ET(PI)T.
-- From Matrix Methods in Optics by
A. Gerrard and J. M. Burch.
I also read about polarization.
I read about linear, circular and elliptical polarization,
birefringent materials, and quarter-wave plates.
Thursday, July 28, 2005
Today I took lots of pictures with Dr. Noé's camera. First,
I emptied out and wiped the table I was going to put my set up
on. I put the monochromator on the table. It's a lab table and now
it's my lab table. Yeah!
Objective: To start with my set up
Basic Equipments: Monochromator, two polarizers, pieces of cellophane, and ?
Accomplishments: I placed the monochromator on the table and
used Dr. Noé's camera to take pictures through a diffraction
grating. I took lots of pictures ranging from 0.70 to 1.60
(monochromator dial setting). I also got to see the inside
structure of the monochromator. There are a light bulb, circular
mirror, a slit and few lenses inside. As you know, humans can
detect light in the range of 400 nm and 700 nm only. Depending on
the number of the monochromator dial setting, colors coming out of
the monochromator change. Also at certain times, through
diffraction grating you can see more than one color because there
are more than one order.
Learn:
Monochromator
Birefringence
Cellophane
Colors in the plastics when viewed with polarizers on above and below
Future: Yo no sé yet.
Color
Management (LightCyan)
For my qutoes
page
Greg showed me where the screws, washers and holders are. He told
me which one to use for which. He helped me find a thing that can
hold a cellophane and can rotate it. I never knew there were so
many equipments in the lab before.
Wednesday, July 27, 2005
So today was the REU tour. We did a lot of cleaning and
organizing. I realized how much dust there was in the lab. I
decided that we should clean the lab at least once a week to create
a fresh and decontaminated environment. My science research
teacher, Mr. Schorn, came to Stony Brook to visit Great Neck North
students today. I visted the engineering building with him and saw
the garcia people. It was pretty cool. I realized how little I know
about polarizers today. I mean the basic things like having three
polarizers. So I did some observations today. I started reading
about the polarizers in Feynman's Lecture: Volume I.
Objective: To understand how polarizers work, without the
cellophane. Try different combinations: two and three polarizers
(linear). Try rotating the middle polarizer and also try rotating
the top polarizer. Try the circular polarizer. Observe and make
generalizations.
Prove: Mathematically, show why, together, two circularly
polarized light in opposite clockwise directionc produce one
linearly polarized light.
Question:
When you have a cellophane film between the polarizers, why does
the color of a cellophane change depending on what angle you are
looking at it?
Tuesday, July 26, 2005
Note: Light is a transverse wave. In other words, a medium's
displacement is perpendicular to the light wave's direction of
motion.
Tutorial
on Polarization.
Today José showed us how to use Femlab a little bit. Femlab
seems to be a very useful tool if and only if you know how to use
it. It makes hot colorful pictures. It can do lots of things with
physics, including calculations. Using the Femlab, José
defined the properties of an object, such as the constituents of
the material. He then chose to apply two distinct forces at certain
points. It seemed that based on the boundary conditions you put in,
the Femlab could calculate lots of things for you. He also showed a
little bit of heat transfer. I asked if Femlab can do the same
thing I did with heat transfer, or calculating temperatures at
defined and equally spaced points, on a spreadsheet. José
said that he thinks it can. That will be cool.
Look up:
Unpolarized Light
Stokes Vectors
Stokes Parameters
Malus's Law
Scattering and Polarization
Refraction and Polarization
Reflection and Polarization
Depolarization
Sources:
One and
Two
Dr. Noé showed me several things. First, we aimed a
polarized and unstabilized laser on a cardboard to observe change
in the light intensity. After the laser was turned on, it made a
light spot, which repeatedly grew brighter, then darker due to the
increasing temperature of a laser. Even though it didn't, my eyes
perceived the spot as getting repeatedly bigger and smaller. We
also experimented with a polarizer on the front. Rotating the
polarizer, we saw that sometimes the laser light got blocked. Then
we sent the laser through a rainbow glass (diffraction grating),
which acted as a beam splitter. Two polarizers were placed in front
of two different light spots created by the diffraction grating. By
adjusting the polarizers respect to the laser, we made the spots to
be the opposite. In other words, while one was getting brighter,
the other was getting dimmer. But after the diffraction grating was
placed, the spot did not completely fade out when we turned the
polarizers, because the diffraction grating acted as a polarizer
and changed the polarization of the beam. I learned what a
photodetector is. Photodetector was connected to the MultiMeter
which measured the current in micro amperes. In a real experiment,
I would have to level things to the same height and adjust
distance, but today, I just held the photodetector and tried to
hold it as still as possible. Number wise, the current kept
inreasing then decreasing, and so on. This demonstration relates to
modes, which I basically know nothing about. Dr. Noé said
that to fully understand what is happening requires a lot of
background knowledge on modes. At one point we also used a piece of
glass to create two parallel beams. By adjusting the glass to be at
a certain angle, two light spots were created because there were
two reflections. One was from the front side and the other was from
the back side. The intensity of each spot, Dr. Noé said, is
about 4% of the original beam. Dr. Noé explained how an
op-amp can be used to control temperatures of a laser: stabilizing
the laser. He showed me the optical part of the setup that would be
required to stabilize a laser. It consisted of a beam splitter, two
small mirrors, and two diodes. The laser needs to be shot at the
beam splitter at a certain angle and at a right level so that each
splitted laser beam goes into its corresponding diodes.
Plan for my project:
My first project is going to involve
layer(s) of a cellophane film and polarizers. I learned today that
when two polarizers are at 45° to each other, and you rotate
the cellophane in the middle, you can see the colors of cellophane
change, clearly. One set of colors was purple and orange and the
other set was blue and green. Resulting color depends on the number
of cellophane layers as well. I am setting my set-up on Thursday so
I can get started with measurements and graphs, etc. First I need
to read more about polarizers and cellophane to understand things
better. This experiment will involve a monochromator, which is
consists of a light bulb and a diffraction grating in an enclosed
setting. By adjusting the knob on the monochromator I can choose
one color at a time. For my set-up, I need to place the
monochromator, two polarizers and a cellophane at the right spot. I
need something to hold the cellophane and the polarizers,
separately. Also it should have a little knob or something that I
can use to rotate the cellophane film or polarizers at precise
angles.
First step: To understand how the polarizers and the cellophane work.
Second step: To observe in different conditions
(ex. different number of cellophane layers, differnt color, etc.).
Third step: To take some measurements and generate graphs; To get data.
Fourth step: To know what Jones matrices are and know how to use them.
Fifth step: To use Jones matrices to explain what is happening
(Each situation will have different matrices)
Once I complete these steps, then I can try other things. One bad
thing about a monochromator is that the intensity of light is too
weak to be measured with a photodetector. Dr. Noé said that
later if things work well, I can use amplifiers to measure the
intensities of light and that perhaps I can build an amplifer using
electronics. But, in that case, things will get much more
complicated.
Monday, July 25, 2005
Over the weekend, I spent a great deal of time reading about
matrices in general, but particularly mueller
matrix imaging (Molly Bright's Intel paper). I did not
understand everything, but the concept of generating colorful
pictures using matrices interested me. How do you convert
mathematical values into colors? Some other questions I had were:
What do the pictures show about a medium? What are the uses of the
pictures? Would the picture look different for the same object at
different temperatures, concentration of something, etc.? Would I
be able to do mueller matrix imaging with a trapped gas? Today
Dr. Noé told me that mueller matrix imaging produces many
nice pictures, but currently, the use(s) of the pictures is(are)
not known. So only thing we can to make generalizations and
conclusions based only on observations without actually knowing why
and how muller matrix imaging works that way.
I also read about Jones matrices, and a little bit about Mueller
matrices. See Jones
calculus. It shows different polarizations and corresponding
Jones vectors, and optical elements and corresponding Jones
matrices. There is the matrix Lindsey and Dr.Noé derived
some time ago. One disadvantage of Jones calculus is that it works
only with fully polarized light. Mueller calculus, like Jones
calculus, uses matrices to observe the effects of optical elements
on light, but Mueller calculus is more complete in the description
of light beams and can be used for unpolarized, paritally polarized
or even incoherent light. Check out Mueller
Matrices of optical elements. As you can see, to represent a
circular polarizer or a quarter-wave plate, Jones calculus uses 2
by 2 matrix with both real and imaginary values (i), while
Mueller calculus uses 4 by 4 matrix with real numbers only.
Today all of us and Dr. Noé worked on writing the first few
sentences of Nilus' report on optical lever project. We worked
together to produce clean and sententious sentences. It took us a
long time just to develop first 3 sentences; We learned how
important wording and structure of a sentence are in a scientific
paper. Later, Greg taught me harmonic motion and how it relates to
RLC circuit. We reviewed damped harmonic motion which I learned
last time. Additionally, I learned forced harmonic motion and
something about beats - which my 10th grade (unsuccessful) research
project was on. Closer the frequencies longer the each beat. Greg
demonstrated this with tuning forks.
Friday, July 22, 2005
Today Nilus and I built a little circuit: Dark-Activated Dual
LED Flasher (p.26 in Digital Logic Projects by Forrest
M. Mims). Its sensitivity to light makes it cool: When you turn the
lights off, LEDs flash, while when you have the light on LEDs turn
off. The description is given below:
"You will add a light-sensing circuit between the
simple LED flasher and the power supply. The sensor circuit will
apply power to the flasher only when the light intensity falls
below a threshold that you will adjust using a
potentiometer."
When we blocked a photoresistor and made the area seem dark, the
LEDs flashed. When we increased the threshold using 1M
potentiometer, the LEDs flashed irrelevant from whether the room
was dark or not. But when you decreased the potentiometer, starting
from a certain point the light only flashed when it was dark.
Professor Metcalf gave a lecture today. Topics included various
things. We discussed about how op-amp works, why these work the way
they work, and how a toilet, feedback system, and diode lasers
work. I read about logic gates
(from Matt's journal). I found logic's relationship with circuit
very interesting, especially because logic is a branch of
mathematics that I have some interests in. I am interested in
electronics, feedback system, and op-amp, as well. For logic
gates, AND, OR, and NOT were easy to understand but NOR, NAND,
etc. confused me.
Thursday, July 21, 2005
Goal: To Do Something
We used polarizers to see sky and trees. With one polarizer,
turning it changed the contrast. At one instant trees were spring
green colored, without light or dark spots. Turning it by 90°
maximized the contrast so I could see light and dark, and I thought
that trees looked very scary and unnatural with so much
contrast. I've never used spreadsheet by myself for real
before. Today, with Dr. Noé I made my first real
spreadsheet which was on heat flow and relaxation methods using
Dos. Today I had 7 by 7 points, which is definitely more
complicated than 4 by 4. Again, I defined top row as 100 degrees,
except for corners, which were 50 degrees, and all other points on
the sides were 0 degress.
I find it very interesting that computer-related things (very vague
here) like html and Mathematica are case sensitive (word
obtained with Nilus' help). Greg just showed me slope field
applets. Today I am 63.25 inches, or 5ft and 1/4 inches. I grew
shorter overnight. Apparently, it seems that the data of my height
needs greater accuracy. Now I know how to write
Dr. Noé's name correctly with an accent on e, liek
this: é. Professor Metcalf gave us our pictures. I
look weird in it but I guess I'll bare with it.
Wednesday, July 20, 2005
In the morning, I tried the LEDs and put them it right places with
the correct color labels. We talked little bit about coherent
backscattering effect at lunch. I asked why it is considered to be so
difficult (for a project). Dr. Noé said that first, phenomenon
itself is difficult to understand. So to briefly describe what it
is in my words: when light enters a media, scattering occurs, and
backscattering, or direct backscattering to where the light
source came from occurs as well. As a result an intensity cone
forms. In order to measure the intensity of the light, you need a
beam splitter because you cannot measure it right in front of the
laser (then you will block the light from the laser)..to be continued..
I got one project idea today, but I am still kind of confused as to
what it exactly is. It involves the built system by Greg and
Amol. It involves optical vortex, mechanics*, matrices, and
polarizers. Right now I am trying to solve temperature flow at
points by hand (meaning without a calculator). Dr. Noé gave
this problem to Nilus and me. Imagine a four by four square metal,
and use dots to represent it. So there are 4 dots in each row and
each column, total of 16 dots. The bottom side is 0 degrees. The
left and right side are also 0 degress. Top is 100 degrees. Two
corners between top and the sides we just made 50 degrees because
we weren't sure as to what they should be. So I'll try my best to
explain what I was doing. Rows will be described by 1-4 and columns
will be described by A-D. So the point on the upper left hand
corner will be A1 and the last point on the bottom right hand
corner will be D4. Most of the temperature points are given
above. To reminisce your memory .. at A1, A4: 50°C; At A2, A3:
100°C; At other boundary points: 0°C Now we assume
temperatures at the points except at B2. Your assumption can be any
number. Then we calculate the temperature at B2 by adding 4
temperatures around it (connecting the points will form a diamond
shape around B2), and dividing the sum by 4. Taking turns, B2, C2,
B3 and C3, we calculate and recalculate aforementioned 4
temperature points. As the calculation continued, digits (behind
the decimal point) kept on increasing; I think the increase in
digits means increase in accuracy... I don't remember for 100% but
I finished when I had about 12 digits. Afterwards, I used a
calculator to briefly check over my hand calcuations, and was happy
with my performance. Today was definitely a fun intellectual
pursuit day.
I have a good news. I am 63.5 inches, or 5ft 3 1/2 inches. So I grew
half an inch. We took group pictures today.
Tuesday, July 19, 2005
Professor Metcalf gave a lecture on time, atomic clocks, laser
cooling, frequency comb, etc. The lecture was so intriguing. I
especially got interested in frequency comb and laser
cooling(!!!). I was interested simply in the fact that you can
use lasers to cool atoms (to be continued..). Yesterday
Dr. Noé said that I can use matrices to observe the
chromatic effects of light that goes through two polarizers with a
layer or layers of cellophane in between them. This idea can have
applications in the arts, and as Maaneli showed me, it is related
to Jessica Newman's project. Here is the abstract. I
also read about optical tweezers today. I am still pondering on my
project ideas. I am definitely interested in matrices and
mathematical side of physics, but I want to generate some graphs
(data), as well. I am going to look up 'matrices and scattering'
and 'matrices and diffraction' to see what other applications of
matrices are there besides polarized light.
Dr. Noé was cleaning the back part of the lab. He made a
table for electronics. We connected two 470Ω resistors in
parallel and connected them to a function generator and an
oscilloscope. We also connected them to a LED. Our goal was to find
out which LED is what color so we'll be able to put the LEDs in
right cases. We tried bicolor LED, which was both green and red -
it flicked back and forth! Maaneli changed the frequency of the
signal using the function generator to change the flicking
speed. In other words, by controlling the frequency, he could
control how fast the LED changed back and forth from green to red
or vice versa. We looked at our simple setup through the
diffraction grating. We saw that red was pure while green consisted
of green, some red, and even a little bit of blue. I also took a
picture by putting the diffraction grating in front of my camera
lens.
Maaneli showed me MIT open courseware (online) which has all course
material plus some video lectures for abundance of college
courses. Here is Electricity
and Magnetism. I am also interested in Linear Algebra.
Monday, July 18, 2005
I decided today that my project will have something to do with
matrices. More specifically speaking, I am interested in Mueller
Matrices. Today, I continued with my work on the webpage, as
usual. I expanded my Other. I typed The Way I Am by
Eminem in it. I added more quotes. Also check out Courses. I
finished making a list of the Mathematics
Courses. That took a decent amount of my life time. Of course,
it's not a complete list, and probably very meager, both in quality
and quantity, but it contains a decent listing of undergraduate and
some graduate level math courses. Today I decided that I am going
to buy a silver Mac laptop. I am definitely going to have
linux. Linux is the coolest thing ever. I'll set it up so that when
the computer starts I will have a choice of using either linux or
Mac OS X.
We had a pizza lunch today with Dr. Noé, Professor Metcalf,
and Dr. Cohen. We discussed where we are heading with our projects
(whether we have any ideas or what we are doing now, etc.) They
helped us by giving some suggestions.
Later, Greg showed me how to solve for an inverse of a matrix. He
taught me reduced row echolon form(rref) and elementary
row operations. Here is elementary
row operations. Also refer to Greg's
journal: week 6. So we found an inverse for 2 by 2 matrix and
then for a 4 by 4 matrix. The latter took some time. In the
evening, I started experimenting with Mathematica. Actually, more
learning the most basic things than experimenting. I just learned
the easiest commands like adding, multiplying, plotting, and powers, square
roots, integral, etc.
Caravelli's Conservation of Contamination: For every
contamination there is equal and opposite de-contamination.
Friday, July 15, 2005
We just messed around with liquid nitrogen. Check Other on
my website. I worked on it. I just put quotes, some literature, poetry,
etc.
Thursday, July 14, 2005
I brought my rap and classical music cds to the lab. Greg brought
all of his Rachmaninoff cds. First, I put on my raps, The Way I
Am, Outta Control, Hate It Or Love It, etc., then I put
classical, Grieg Piano Concerto, Tchaikovsky Piano Concerto,
Schumann Piano Concerto, etc. From Greg's cds, we listened to
Rachmaninov Suite No.1, Piano Concerto No.2, Preludes, and
Sonata No.2. It was very nice to listen to music in the lab.
Nilus and I did a little observation. Our goal was to observe the
change in diffraction pattern when laser goes through water. Nilus
filled about 2/3 of the container with water. The laser was shot to
the mirror and reflected beam was sent through the water, which was
being supported to match the height of the red laser. I took lots
of cool pictures, which I plan to put in my journal sometime next
week. After a long lunch at Jasmine, everybody was gathered around
this little observation. Greg put his remainder of mango lassi in
the water for clearer detection of laser light. We also
experiemented with portable green laser light. We shot it at
different angles. One cool thing was that through water we could
see the light traveling. We saw internal reflection and
refraction. I read a little bit of the Multivariable Calculus book
(by Tom M. Apostol), which Greg and Maaneli found for me at the
library yesterday.
I went back to the dorm and slept for about an hour or
less. Afterwards, Lindsey and I walked to the soccer field to play
soccer with the Laser Lab people and REUs. We played for about an hour
and a half. Even though I sucked, it was a hell of a fun. I am planning to
attend all soccer meetings from now on.
Back
of my head during Professor Metcalf's lecture
and Back
view when deriving Euler's Formula.
Wednesday, July 13, 2005
Today was our first pizza lunch. I had a competition with Greg on
who will eat more pizzas. I lost badly and sadly. I ate 6 and he
ate 8. Jan originally from Germany was our guest speaker. I learned
two German words: Schadenfreude is taking delight in other
people's bad luck. Seruus is a cool way (slang) of saying hi
and good-bye.
Matt and I used the electric kit to build a Percussion
Synthesizer and a Random Number Generator. To
build the second one we unplugged the first one. Percussion
Synthesizer was in Basic Electronics Workbook I (p.78-79)
and Random Number Generator was in Digital Logic Projects
Workbook II (p.82-83). Both books are by Forrest M. Mims and from
RadioShack. What's so cool about our Random Number Generator is
that we attached 5 LEDs, red, wider red, green, white, and blue to
the springs (through which current run) that these 5 LEDs flick as
well. Our work is colorful and pretty sight.
I bought two books yesterday. One is Matrix Methods in
Optics by A. Gerrard and J. M. Burch, and Modern Optics
by Grant R. Fowles is the other.
Tuesday, July 12, 2005
After the fire drill, we used magnifying glasses to burn black
papers. We also saw sun and clouds through it on a white paper.
I showed the notes I took yesterday from Greg's lessons on
simple harmonic motion and differential equations to one of my
friends. When he saw k/m=ωo2, he
asked what ω stood for and I replied, angular frequency. Then he
asked how springs have angular frequencies if they are not moving
in a circle. Well, at that moment, the only thing I could say was
"I don't know." So today, I asked Dr. Noé a similar question:
Why do waves have ω?
Reason: Something waving or oscillating is moving in a circle. This
relationship is shown by
eiθ=cos(θ)+isin(θ). θ on
the left part of the equation needs to be in radians. Since θ
is in radians, we use ω=2πf to convert f(s-1)
into radians. Here comes trigonometry. Imagine a unit circle. Let's
say that there is a point P on the circle. What happens to
cos(θ), the horizontal component of P, as the point moves
around a circle? First, cosine value starts as +1. Then it
decreases, reaches 0, and starts increasing in the negative
direction. It reaches -1, then it starts to increase, or decrease
in the - direction. It passes 0 and continues to increase in the +
direction, reaching +1 again. Cosine will repeat this pattern
indefinitely while sine will repeat its own pattern. Now imagine a
cosine graph. It oscillates. So does spring. Spring oscillates. To
conclude, Dr. Noé said that mathematically, waves are
in circular motion. So beautiful and so mysterious - mathematics.
I read about Coherent
Backscattering Effect from past projects. It's not a
consideration for this year's project, but it is a topic I
plan to keep some interest in.
Monday, July 11, 2005
I have never learned so much in one day before. Also, today I
actually understood most of the things that went on and I didn't
get tired or bored either. I gave my full (or closest to full if
not totally full) concentration. To summarize, it was an awesome
day. Greg was my private knowledge tutor. I also wrote my name in
rainbow colors on the board.
In the morning, I read the black book: Optics by Hecht. I
read about diffraction, and some mathematics behind it. I looked at
the diagrams. I learned how to derive
θ=mλ/a (a-the distance between the slits).
I continued to read on how to derive one-dimensional differential
wave equation. Greg taught me a little bit of multivariable
calculus last time. Today he showed me how the partial derivatives
worked and how to derive the differential wave equation, because
the book confused me. He also showed me two and three-dimensional
differential wave equations.
One Dimensional Differential Wave Equation
(This does not show the cool derivation, but at least it shows the formula)
Dr.Noé taught us some mathematics involved with waves. Wave
is both space and time dependent. Knowing f(x)=Asin(kz-ωt),
k=2π/λ and ω=2πf=2π/τ, we derived phase
velocity, v=λf=ω/k. We learned how wave itself can
move faster than light. More complete equation for a wave is given
below:
ψ(x,t)=Asin(kz-ωf+φ)
A, the amplitude, is the factor that moves the function up and
down. φ is the factor that moves the function left and right.
Of course, we did even more of the cool stuff. We learned how to
calculate the intensity of the waves that passes through two
slits. We derived
I=2A2[1+cos(kxd/L)]=2A2[1+cos(kdθ)]. The
second equal sign has to be wiggly because it's an
approximation. We also got x/L=λ/d, and
dθ=l1-l2.
(d is the distance between the slits; l1 is the distance
between the first slit and point P; l2 is the distance
between the second slit and point P; L is the distance between the
slits and the wall far far away; x is the distance from the middle
to some point P above it. θ is classical θ. It will
be much easier to understand with a diagram.)
Greg taught me some really cool3 physics stuff. He
taught me how to solve some simple harmonic motion problems using
differential equations. I was given a diagram and boundary
conditions, and asked to find a general solution and equation of
motion. He also taught me what characteristic equation and linear
ordinary differential equation (ODE) are. I got two homework
problems, which I solved in the lab with Greg's help. The last
homework problem was damped harmonic motion. I learned about
underdamped, overdamped, and critically damped conditions, and how
these situations can be applied to real life objects, such as a
door and a car (Applied Physics?). I learned how to derive
x=(vo/ωo)sin(ωot),
and τ, the period of the
spring: τ=2π(m/k)1/2. (vo/ωo is an amplitude)
Natural Frequency
(This shows some of the derivation)
Friday, July 8, 2005
Today was a bad and a good rainy day. Bad part: raining. Good part:
staying at the SAC for a long, long time, problem solving. Amol,
Lindsey, Maaneli, and I sat on the same side of the table. After
lunch, we started sharing riddles and problems. It was really fun
(The best part was suggesting illogical or unreasonable solutions
to the problems). Anyway, we did lots and lots of problems. My
favorite one was Amol's one about two black people and two white
people who are stuck in the ground. It goes like this:
None of the four people knows what color he is, but each knows that
there are 2 black and 2 white people. Each of their quest is to
find out what color he is and yell it out. But there is only one
person who can do this, and our goal is to find this
guy. Description of the physical situation is like this: Each can
only see the head(s) of the person(s) in front of him. Thus,
each only knows the color of the person(s) preceding him. Exception to
this rule is that there is an infinitely high wall between the
first two people. The 1st person can only look at the wall; thus,
he cannot see anybody. 2nd, 3rd, and 4th person on the other side
are also looking towards the direction of the wall. They cannot
move their heads to check out the color of the person behind
them. None of us solved this problem, but it was a good problem. It
just requires some thinking.
One of Lindsey's problem was this:
Mary comes back to her home and finds Emily dead, lying on the
floor, and finds Sam asleep on the couch. There are broken glasses
and water on the floor near/around Emily. What happened? (all the
names are made up)
Maaneli's problem:
You have 6 coins. Organize these coins in such a way so that
there are 4 coins in two directions.
There were other cool problems, but either I can't remember them or
I can't explain (write about) them explicitly. To get an answer to
one of the above problems just ask one of us who was there.
Thursday, July 7, 2005
We had a short lesson with Professor Metcalf on waves. I said that
it's difficult for me to understand how they exist. Both waves and
edges of a card board are wiggly lines but what distinguishes these
two is that waves move. Waves depend both on space and
time. We pondered upon the idea what is transferred through the
waves. What actually moves? We learned that waves transport
information. Then this question came about: What is information?
Professor Metcalf told us that information is like time, somthing
that we know but find hard to define; he quoted St.Augustine: "I
know what time it is as long as nobody asks me."
f(z)=Asin(kz-v(t2-t1))
One thing we were told several times was that sine and cosine waves
are related. Eix=cosx+isinx and cos(90-x)=sinx are two
famous examples of this relationsip. Dr.Noé said we'll learn
how to write waves in terms of complex numbers. I am very eager to
learn that (Abstract waves getting combined with more solid
mathematics). Greg and Dr.Noé told me not to think about
light in terms of photons yet. Dr.Noé said that things get
very confusing at that level. Greg taught us some basics of modern
physics, which was part of my 9th grade physics curriculum, but I
failed to remember. He said that there is a thing called cutoff
frequency, below which no energy is emitted. E is proportional to
f, and I is proportional to the number of particles. E=hf. For
example if ultraviolet light is shot to a certain metal, electrons
will be emitted. If radiowaves were shot to the same metal and no
electrons came out, then however much the intensity of radiowaves
is increased, there is no electron emission. Increasing the
intensity of radiowaves will only increase the number of photons.
We had a long lunch at Jasmine. When walking to Jasmine, we talked
about circular polarization. On the way in we looked at the water
ripples produced by fountains of the Wang Center. I have never
given much thought to ripples before. But when I saw the ripples, I
remembered reading about them in the Laser Lab sometime last
week. Seeing the interference pattern was cool. I guess knowledge
changes how you view the world. Dr.Noé said something like
that yesterday. Today he said that knowledge begins with accepting
that you don't know something (actually a lot of things), but
realizing that you can find it out. I believe that wonder triggers
research, but persistence and determination are those that make it
possible, determining the results.
Circular
Polarization
So my question is: What am I curious about? What is something that
I am really interested in? Something that I can think about and
experiment with for months.
Wednesday, July 6, 2005
Maybe I'm not suppose to write about this, but this morning I swam
in the Sports Complex to practice my survival skills, because I am
a bad swimmer. After that, I continued my experimentation with
css. Now my web page's background color is paleturquoise instead of
palegreen. We ate lunch at the SAC. After I finished my hamburger
and stuff, I ate Haagen-Dazs ice cream. When I was almost done with
it, I realized that it contained: 350 calories, 280 calories from
fat, 30% cholesterol, 45% fat, 75% saturated fat; this is as far as
my memory permits me. So I decided never to eat Haagen-Dazs ice
cream again for the rest of the summer. Also, something weird
happened. In the morning when Nilus measured my height I was 64
inches, 5 ft and 4 inches. After lunch, when I was remeasured,
everybody agreed that I was 63 inches, 5 ft and 3 inches, or
less. I grew an inch shorter today. Hopefully I'll be able to catch
up with 2 inches tomorrow. Anyway, from now on I am going to
measure my height every week to see if I grow this summer.
Dr.Noé showed us how to use Dos (ex. creating a
spreadsheet data). It was very fun, because I didn't know
spreadsheets were capable of so many tricks. Dr.Noé showed a
demonstration by graphing the data we obtained yesterday. We
learned how to create a best fit line, how to calculate error, or
'goodness,' and many more.
Tuesday, July 5, 2005
Professor Metcalf gave us his second lecture today. He started like
this: All numbers commute, but there are some things that do not
commute. Among the things that do not commute are operations and
transformations. One example of such operation is matrix. Addition
of the matrices is commutative, but multiplication of the matrices
is not. We learned some basics about matrices, how to add and how
to multiply them. It was very cool. We learned that matrices are
used to represent polarizers and electric vector of light. For the
rest of the day, we had even more matrices. Dr.Noé and
Lindsey calculated this cool matrix for representing a polarizer at
an arbitrary angle θ. Dr.Noé taught us basics about
screws, breadboards, etc. Nilus, Maaneli and I did a little
experiment.
Check out Identity
Matrix.
HW#1 Find all square roots of I2
HW#2 Repeat the experiment Professor Metcalf demonstrated with book
and paper cup (something that has a rotational symmetry). Think about
how sometimes some rotations commute depending on an object. What if
you have rotation about 3 axes?
Friday, July 1, 2005
I got my student id today, but my picture is depressing. Learning
linux, html, and css -- These are so interesting especially because
I did not know of their existence before the Laser Lab.
Trigonometric Formulas
Thursday, June 30, 2005
Professor Metcalf taught us some mathematics. We learned about
square roots, cube roots and on, imaginary numbers, series
expansion and complex numbers. He also showed few simple
demonstrations with the polarizers (2-3) to show how different
angles allow different fraction of light waves to go through while
others block the light waves. Dr.Noé said that we can
measure how much light actually comes through the polarizers (I am
interested in this). Dr.Noé taught us elementary polar
coordinates. We learned how to use eix=cosx+isinx to
derive trigonometric identities.
How to derive
Euler's Formula
HW#1 Find all solutions to 8(1/3)
HW#2 Define Number. What is a number?