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

Why is the work significant?

provide a brief review of most relevant literature

cite all relevant literature

info. on concurrent similar or related work/project in the laboratory

Describe the methods used to allow someone trained in the field to understand

What was done

How it was accomplished

result of research

How result addresses the problem to be solved or research question to be addressed

Discuss any interpretations that can be drawn from the results

What questions still need to be answered?

Does the Research report have a basis for future work?

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 so^99999999999 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(n_e-n_o)/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, n_e the index of refraction of an extraordinary axis, n_o 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, n_slow and n_fast, 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 = O^TY^T. Using that and the assoicative law for matrix multiplication, you can prove (ABCDEF)^T = F^TE^TD^TC^TB^TA^T. For example, (PIE)^T = [(PI)E]^T = E^T(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.

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=ω_o², 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 e^iθ=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:

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=(v_o/ω_o)sin(ω_ot), and τ, the period of the spring: τ=2π(m/k)^1/2. (v_o/ω_o 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. E^ix=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 e^ix=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?