JournalNovember 10th, 2009After a long layoff from working in the lab, it's time to get working again. I still have a bit of data to take, such as measuring the intensity of the evanescent wave at different angles away from the critical angle. So far, my project is just a duplication of an AJP paper (link in previous entry), so I wish to put an interesting twist on my work. I'm going to start working on my web report at the same time. August 12th, 2009I created a new page with my web report on it (see home page for link). I have uploaded pictures of my setup. The first part of my project does not involve taking data on the evanescent wave. Instead, I am taking data on the light that is transmitted through the two prisms before the critical angle. Because the prisms are mounted on a translation stage, I am measuring the intensity of the transmitted light as the air gap betweent the two prisms is varied. The resulting data should resemble a series of oscillations which can be seen visually when viewing the fringelike interference patterns between two glass plates. The data will be entered into the web report. August 11th, 2009For the most part, the setup is together. Two right angle prisms are placed on top of a turntable equipped with a vernier that can measure to within five minutes (1/12) of a degree. The turntable is placed on a micrometer translation stage. A rotating polarizer is placed between the laser and the prisms. A photodetector connected to an ammeter is placed on the other side of the prisms and is used to measure the intensity of the transmitted light. The prisms are pressed together by two rubber bands and a Ni foil spacer of around 12 microns is used to create a wedge between the two prisms. We have observed frustrated total internal reflection/optical tunneling already. I am currently taking data on the strength of the light transmitted through the prism when the incident light beam is not yet at the critical angle. The data should yield a sinusoidal curve as the width of the air gap between the prisms is varied. One rather annoying problem is that the reading on the ammeter doesn't stay still and fluctuates rapidly. I am just going to take the minimum value of the readings so that the trends should still be accurate. Here is the article that the describes the experiment I am duplicating: Click Here August 10th, 2009The right angle prisms arrived today. I decided to check to see if the prism was indeed made of BK7 glass using the critical angle method. My measurements yielded an index of refraction of 1.517 which is very close to that of BK7 glass (1.515). I did notice that the two prisms were not the same size. I wonder if this makes any difference... Just a random thing I wanted to say, Ubuntu Linux is a terrific operating system! To download, go to ubuntu.com. Once you download the file, burn it to a disc and the installation helper leads you through the simple process. Sebastian gave me a couple of commands to optimize Ubuntu, type them in on the terminal:
August 7th, 2009I measured the critical angle of the prism once again using an optical turntable. Our previous method (see July 29th) yielded a refractive index of 1.532. Using the optical turntable, which can measure angles to within 5 minutes of a degree, I calculated the critical angle of the prism to be approximately 40.56°, and this gave n = 1.537. A source of error is the ambiguity of determining where the critical angle occurs. I rotated the turntable until the transmitted light disappears; however, the precise location where the light disappears is slightly ambiguous. Today is Woody's last day and also the end of the REU program. Most of the REUs will be back next week to continue their research. Woody is going back to Virginia; hopefully we will see him again. August 6th, 2009  Newton's RingsWe saw Newton's rings today! I need to get a copy of Newton's Opticks. I'm currently planning out my project and familiarizing myself with some of the tools I will be using. July 30th, 2009  Prism DataJuly 29th, 2009  Measuring the Refractive Index of a Prism of Unknown MaterialSorry I haven't updated in a few days. Woody and I have been busy trying to measure the refractive index of a prism because we don't know what it is made out of. There are two theories as to what the prism is made of: crown glass or fused silica. The method using the angle of minimum deviation (see July 22nd entry) doesn't work for this prism because the refractive index is too large. This can be proved because the trig functions have a limited range. The method we used utilizes the critical angle to find the refractive index of a prism. We shined a laser through the prism and rotated the prism until the transmitted light disappeared and total internal reflection occured (the critical angle). We then put a piece of cardboard in front of the laser and poked a hole where the laser beam intersected witht he cardboard. We then marked the spot where the reflected beam (reflected from the face of the prism) hit the cardboard and therefore measured the angle of incidence. We measured the distance between the laser beam and the reflected beam. Then, we measured the distance from the cardboard to the prism. Using simple right triangle geometry, we were able to find the critical angle of the prism. Our Excel spreadsheet yielded a refractive index of approximately 1.532. The refractive index of crown glass is 1.52. To ensure that our result was accurate, we repeated the experiment a second time, making sure everything was perpendicular or parallel as needed. In addition, we calculated the minimum and maximum bounds for our value of the refractive index of the prism by plugging our measuring error into our spreadsheet. We varied each length by 1 mm, the error of our distance measurements. This yielded a minimum value of 1.531 and a maximum value of 1.533, pretty insignificant for our purposes. To further ensure that this prism was made out of crown glass, we took Dr. Cohen's advice and measure the density of the prism by finding the mass and the volume. This turned out to be harder than it seems because a metal was glued to the base of the prism. Ethan managed to heat up the prism and break the bond between the prism and the metal and Woody was brave enough to take some pliers to the metal. We found the density to be 2.391 g/cm^{3} or 2391 kg/m^{3}. The density of crown glass is 2400 kg/m^{3}. We could pretty much conclude that the prism was made of crown glass. Such measurements aren't trivial. Andrey measured the refractive index of the prism using another method and had to ensure accuracy by comparing his results to ours. July 24th, 2009  Frustrated Total Internal ReflectionIt's interesting that total internal reflection does not exactly reflect all light. A field, called the evanescent field, forms where a transmitted beam would have occured. This evanescent field is similar to a light wave except it doesn't propogate and has "no" energy. This evanescent "wave" can be trapped if another medium of equal refractive index to the first medium is placed somewhere within a wavelength of the first medium. The trapped evanescent wave can then make its way into the third medium. This phenomenom is called frustrated internal reflection. Picture from http://www.uvm.edu/~dahammon/whatsnew/whatsnew04.html July 23rd, 2009Using the same setup from yesterday, Woody and I decided to look for a relationship between the refractive index of water and the water temperature. As the graph shows, an increasing temperature results in a decreasing index of refraction. The left vertical axis (distance) is the distance opposite the angle of minimum deviation (the side that is 147.955 cm in yesterday's diagram) which is used to find the angle of minimum deviation. July 22nd, 2009Woody and I used this setup to measure the refractive index of water in the prism shaped box. The laser beam is reflected off of a mirror (bottom right) and directed towards the prism. WALL ON THIS SIDE We measured the angle of minimum deviation to be 50.5836° by measuring the two distances shown above and using the inverse tangent function. With the angle of minimum deviation, we were able to use the formula (from yesterday's journal entry) to find the refractive index of the water in the prism. Our calculations yielded a n_{p} (refractive index of the water) of 1.331372172. I don't quite feel like using significant figures... The accepted value of the refractive index of water is 1.33. The reason our experiment was accurate is because of the concept of angular size (see June 30th entry). Because the wall was a good distance from the prism, we were able to make an accurate measurement of the angle. A few centimeters translates into a small fraction of a degree. Therefore, if we were to repeat the experiment a greater distance from the wall, we would be able to achieve even greater accuracy. The experiment was not as easy as it seems. First, we had to make sure the laser was parallel to the wall so that the beam reflected off the mirror would be perpendicular to the wall. In order to ensure this, we placed a mirror on the wall and adjusted the other mirror so that the reflected beam would take the same path back to the laser. Measuring the side of the triangle opposite &theta_{md} was easy. However, measuring the side adjacent to &theta_{md} was a bit more complicated. Because we had to measure from a precise point in the prism where the refracted and unrefracted beam met the triangle's perpendicular bisector, we decided to trace the image of prism on a piece of paper and draw the perpendicular bisector geometrically. With the prism still removed, we placed a screen where the beam intersected the bisector and measured the distance adjacent to &theta_{md}. July 21st, 2009Today, I found an equation that could be used to find the refractive index of a liquid inside the prism box. I was curious to find out how it was derived so I asked Tom to help me out. We started out with this diagram: In this setup, a laser passes through the prism and is aligned so that the ray going through the prism is parallel to the base. The known variables are &theta_{p} (apex angle of the prism  the angle corresponding with the base of the prism), &theta_{md} (the minimum deviation angle  angle between the line drawn if the laser passes straight through the prism and the line extrapolated by the refracted beam), and n_{0} (indices of refraction of the outside substance  usually air). We can then use the following equation to find n_{p}, the index of refraction of the liquid in the prism July 20th, 2009So, what happens if I use white paint instead of nondairy "whitener" (creamer) in a mixture with the water? July 15th, 2009  Simulating a RightTriangle PrismIn my last journal entry, I talked about the righttriangle prism and the total internal reflection that light undergoes when it goes through the prism. Dr. Noé found a large plastic righttriangle box and told us that we could simulate the path a laser light takes through the prism by filling the box with water and some coffee creamer. I tried it today and sure enough, we were able to see the total internal reflection through the prism (picture below). The laser is entering the creamer/water mixture until it meets the glass/air barrier where it is total internally reflected. Then, I tried to simulate the effect of light going through a prism like the one below (without the dispersion effect because I used a laser) and noticed that indeed, the light came out at the same angle as it entered. I want to try to get a dispersion pattern (rainbow) out of the prism next. Also, I remember Dr. Noé saying that this setup could be used to determine the refractive index of certain mixtures and fluids. I want to look into this further. July 13th, 2009  Making Elliptically Polarized LightIn this setup, linearly polarized light from the laser passes through a prism. According to Snell's Law, n_{1}sinθ_{1}=n_{2}sinθ_{2}. When θ_{1}=0°, θ_{2} must also equal 0° ;therefore, light passes straight through the glassair medium without any refraction. The interesting thing is that although the light entering the prism is linearly polarized, after the light undergoes total internal reflection, the emerging light becomes elliptically polarized. At first I was a little confused as to why this happens. Dr. Noé pointed out that this occurs only when the electric field of the entering light is not strictly vertical or horizontal. Therefore, this entering light is a combination of two electric field vector components. Each one of these components undergoes a phase shift until they are 45° out of phase, resulting in elliptical polarization. Fresnel's Rhomb uses this concept by passing light through two prisms, creating circularly polarized light. July 9th, 2009  Proof Explaining Two Image LocationsDr. Noe showed us this different version of the familiar thin lens equation a while ago. I just figured out a way to put up equations (see equation editor link under my links tab) so I'm going to put it up now. It clearly shows that there are generally two image locations when a lens is used to project the image of a light. In addition, one could use this derivation if the focal length of a lens and the distance (d) between the object and the image are known. I think this equation is pretty cool. However, if one does not know the focal length of a lens, this equation is pretty useless. I found another equation that can be used to find the focal length of a lens: n is the index of refration of the glass that the lens is composed of. R_{1} and R2 are the radii of the two spherical surfaces that make up the lens. July 8th, 2009  Christiansen Effect/FiltersI plan on reading up a bit more on the Christiansen Effect. I found this definition online: monochromatic transparency effect when finely powdered substances, such as glass or quartz, are immersed in a liquid having the same refractive index. Here is a picture of a Christiansen Filter: July 7th, 2009  LinuxWith some help, I was able to learn the basics of Linux and spent the whole day setting up this website. It took me quite a while to determine the optimal background color, I settled on dark slate gray. July 1st, 2009  Gathering KnowledgeHere are some things that I learned today: Elliptical polarization occurs when two perpendicular Efields of light are out of phase. Circular polarization, a special case of elliptical polarization, occurs when the Efields are 90° out of phase. A retroreflector reflects light in a way that the reflected ray is parallel to the incoming ray. A retroreflector consists of three mirrors, all perpendicular to each other. When you look into a retroreflector, you can see that your dominant eye is aligned with the "crosshairs" at which the three mirrors meet. Retroreflectors have many uses. For example, in laser range finding, a laser is shot from the rangefinder to a retroreflector which returns the light. The colors in rainbows are formed by the changing index of refraction (dispersion) of the water droplets with changing wavelength. The bow shape is formed because the refracted light emerges at an angle of around 42° with respect to the incident light, regardless of where that light enters the raindrop. If you were flying in an airplane, you could see a rainbow in a full circle. Just a few questions I intend on answering: What is a purple bow? What is a caustic? Also, I read an article today on chromatic dispersion. This occurs when a mixture consisting of two materials with the same refractive index but different dispersions is created. Apparently, a solid line of color forms as a result. I would like to look into this further. June 30th, 2009  The Angular Size of an ObjectThe angular size of an object is calculated by the equation θ d/r Because the path the sun travels is so large, we use the diameter of the sun as length of arc. The mean distance from the Earth to the Sun (r) is 1.5x10^{11} m, while the diameter of the sun (d) is 1.4x10^{9} m &theta=l/r Therefore, using the above equation, the angular size of the Sun is approximately 0.00933 radians. The angular size of the moon is 0.00895 radians, which explains why the moon can block the sun in a solar eclipse. The ratio of a diameter of 1 cm and a radius of 1 m gives an angular size of 0.01 radians. When we went outside, we experimented with this fact by blocking the sun with a piece of paper that had a pinhole in it. We projected the image onto a piece of black paper. When the image of the sun was approximately one centimeter in diameter we observed that the distance from the image to the pinhole was approxiately one meter. If you were to calculate the angular size of the image from this approximation, you would get 0.01 radians, or 10 milliradians. This is the angular size of the sun! June 29th, 2009  1st DayFirst day in the lab!  
