Group2_8_ch27-32

Lab: Diffraction and Interferencetoc Group: Erica Levine, Richie Johnson, Rebecca Rabin, & Steven Thorwarth Date: 02/02/2012

OBJECTIVE The purpose of this experiment is to examine the diffraction and interference patterns formed by laser light passing through a single slit, diffraction grating and a double slit and verify that the positions of the minima or maxima in the resulting pattern match the positions predicted by theory. In addition, you will compare the diffraction and interference patterns formed by different wavelengths of laser light and different slit widths/spacing.

HYPOTHESIS w/ Rationale The equation d*Sinθ=mλ defines the relationship between many variables within our experiment. While using a single slit, d will represent the width of the slit. While using a diffraction grating, d will represent the difference in lines of spacing. While using a double slit, d will represent the slit spacing. For all single slit, diffraction grating, and double slit, θ will represent the angle opposite the fringe's and adjacent to the distance between the screen and laser, m will represent the integer of fringes, and λ will represent the wavelength of light. Experimentally measuring the d, θ, m will derive the experimental wavelength, which will then be compared to the theoretical wavelength. In addition, it is important to note the relationships between each variable. Increasing the wavelength, will have a direct relationship with the length of the fringes. Increasing the d values, will have an indirect relationship with the length of the fringes.

PROCEDURE Materials To ensure successful completion of this experiment, several materials are necessary and important. An optics bench is crucial for the base of this setup and should always be placed on a flat surface. In addition, a screen must be attached to one end of the bench. Later, this screen will be the area in which the patterns of the laser are projected. In order to begin testing, a single slit, diffraction grating, and double slit are all necessary. They will each be placed on the optics bench (opposite of the screen) during separate testings. We will also need multiple lasers, with varying wavelengths. These will be projected through the single slit, diffraction grating, or double slit and the pattern will be revealed on the screen. A white piece of paper is then needed to trace the pattern produced as well as a meter stick to take proper measurements.

Methods To setup up the experiment, place an optics bench on a flat surface with an optics screen on one end of the bench. To begin testing, place a single slit on the opposite end of the bench. Then shine a laser light through the single slit in the direction towards the screen. (Reminder: The lights should be off at all times in order to produce the best patterns possible) The patterns should be produced on the screen. At this time it is important to trace over the patterns, recording proper measurements including the distance between the screen and the single slit, the wavelength, and the length of fringes. Using the single slit, repeat process using multiple lasers with varying wavelengths. After collecting data completely, replace the single slit on the optics bench with a diffraction grating, repeat process, and then replace once more with a double slit.

DATA (Additional Data Collection Courtesy of Groups 1 and 2)

Single Slit Interference Diffraction Grating Double Slit Interference Single Slit Diffraction Grating Double Slit
 * Additional trials taken from other groups

CALCULATIONS ANALYSIS

DISCUSSION QUESTIONS

- Produced a bright central maximum with consistently dimmer maximums on both sides - Produced a bright central maximum with consistently dimmer maximum on both sides. Within each maximum, light and dark bands were observed. - Produced equally spaced dots running parallel from the center in each direction.
 * 1. Quantitatively describe and compare the patterns produced by:**
 * a) The single slit**
 * b) The double slit**
 * c) The diffraction grating**


 * 2. Make a chart to describe the** //**changes**// **that occur when:**
 * a) the double slit width is increased**
 * b) the double slit separation is increased**
 * c) the slit width of the single slit is increased**
 * d) the diffraction grating lines/cm is increased**
 * e) The wavelength of the light source is increased**



CONCLUSION The results of our experiment prove our hypothesis correct for a single slit, double slit, and a diffraction grating when using varying wavelengths. To test the affects of light when it shines through these three types of holes, we shined a laser through each and recorded the relative location of dark fringes. With this data for multiple wavelengths (3) we were able to prove the equation d*Sinθ=mλ true for all three. For all three scenarios the θ, m, and λ are always the same where θ is the angle, m is an integer, and λ is the wavelength. The d, however, varied with each experiment. In a single slit experiment, the d is the width of the slit and the equation can be written as w*Sinθ=mλ. In a double slit experiment, the d is the distance between the two slits and the equation remains as d*Sinθ=mλ. For a diffraction grating, the d is the distance between slits and is written as a*Sinθ=mλ. When we do the experiments we measured the distance of the fringes from the center of the light that shines through. With a known wavelength, d, and m, we can calculate what θ should be and compare it to the distance and θ that we measure in the experiment. To properly test this equation we tried multiple different trials by changing the wavelength, the value d, and the integer m fringe being measured. Our final data was not perfect but it was pretty accurate, having a percent error of less than 10%. This error was caused when tracing the light in order to measure the distance between the fringe and the center of the light shown. This was done by holding a paper against the sheet and drawing sideways to show where the light is. In this process however, the paper would shift, and it was difficult to draw on the paper without getting in the way of the light shining on the paper. This could be fixed if there was an easier way to measure the distances, such as by having a meter stick directly attached to the screen. This way there would be no sliding or moving the light being measured, and the measurements could be taken directly of the light itself, rather than tracing the light to measure it. This type of experiment is important when trying to shine a light, specifically an image. Single slit and double slit lighting can be used on video projectors to display an image on a wall, such as in a movie theater.

Lab: Photoelectric Effect and Planck's Constant
Group: Erica Levine, Richie Johnson, Rebecca Rabin, & Steven Thorwarth Date: 02/09/2012

OBJECTIVE Determine Planck's Constant Using Stopping Potentials

HYPOTHESIS w/ Rationale As the frequency of a light in a circuit increases, the kinetic energy caused in the circuit will increase in a direct proportion equal to Planck's Constant. This hypothesis is based upon the concepts of Planck in which E is proprtional to nf, where f is the frequency and n is an integer. This value can be seen as the slope on a graph of f v. Ke, and will equal 6.626E-34

PROCEDURE Materials To run this experiment we need a functioning circuit with multiple (4) LED's of different wavelengths to test. We start with a variable power supply in which we can increase the voltage by very small intervals. We then need wires that can connect the power supply to the diode. Next we need an ammeter to measure the current in the circuit to a very small interval (milliAmps). We will also need a volt meter which can measure the amount of volts running through the current.

Methods In order to test our hypothesis we need to run the minimum amount of current through an LED. We can do this by creating the circuit seen in the pictures below. We place a variable power supply on the desk and with wires, connect an ammeter to the circuit in series to the diode. We also place a voltmeter in parallel to the diode. Starting from zero volts, SLOWLY increase the amount of voltage running through the circuit until the ammeter reads the smallest current possible, which for us was a reading of 0.01 milliAmps. The voltage at this instance, as measured with a voltmeter, is the kinetic energy, KE, closest to the stopping potential. Repeat this process of finding the minimum KE for multiple wavelengths (different colored LED's). The graph of these different f v. KE values will have a slope that is equal to what we are trying to solve for (Planck's Constant).

DATA



GRAPH

This graph follows the patten of y=mx + b. The slope represents Planck's Constant, while the y-intercept represents the work function of the particular medal we used in this experiment. It is logical for the graph to follow a linear trend because of the equation, where KE is the maximum kinetic energy, //f// is frequency, h is Planck's Constant, and is the work constant. Our graph displays an R-squared value of .95, indicating that our data is fairly accurate.

CALCULATIONS CONCLUSION As stated in the hypothesis, the direct proportion between frequency and kinetic energy should be equivalent to Planck's constant. Therefore, after properly and sufficiently collecting our data and graphing Frequency vs. Kinetic Energy, the slope produced from this graph should have also equalled Planck's constant. Our slope equalled 8.4E-34. Given that Planck's constant 6.626E -34, it would seem as though our conclusions were extremely off base. However, although their may be a 26.7% error, our experimental value reaches the same exponent and therefore our hypothesis can be stated proven correct. This extreme amounts of error could have come from many different places. It is extremely important to note that this experiment called for the smallest possible current and given this there could have been unaccounted for current. Our concluded results would than be much higher than it would be if there was the correct amount of current. It is also very possible that the tools we used were flawed. Multimeters and voltmeters constantly break and occasionally produce inaccurate results. Much more advanced equipment would need to be used in order to produce the correct amount of current and avoid these many errors. The LED lights used in this experiment are extremely useful in many relevant real-life applications. Replacement light bulbs have been made and LEDs are used as street lights and in other architectural lighting where color changing is used. LEDs are also used frequently in aquariums. Aquariums used LED lights because it allows for an efficient light source with less heat output which allows the aquarium to maintain a proper temperature for animals climates.

Lab: Human Hair
Group: Erica Levine, Richie Johnson, Rebecca Rabin, & Steven Thorwarth Date: 03/01/2012

OBJECTIVE What is the width of a single human hair?

HYPOTHESIS w/ rationale

PROCEDURE Methods and Materials There are many materials vital to a successful completion of this lab. A single strand of human hair, an open lens holder, a white screen, an optics bench, a ring stand, a piece of white paper, and a laser will all be essential to collect significant data. First, take the piece of hair and attach it through the open lens holder. Once this is done, place the white screen and lens holder on optics bench a chosen distance apart. It is then important to position the laser behind the optics bench on the ring stand so that the beam runs straight through the hair. A pattern should be projected onto the screen and at this point cover the screen with a white piece of paper and trace the pattern. Using this data record appropriate values and solve for width of hair. Repeat this process using 2 different color lasers. DATA SAMPLE CALCULATIONS

CONCLUSION Based on the results of our experiment, we calculated that the width of a human hair is 0.0000418 m b using the equation. When we compared this to the theoretical value for the width of the hair, we found a percent difference of 2% which indicates that the data is very consistent. When we found the theoretical value as .0000418m, we knew that this was within the correct range of lengths for human hair. To find the width of the hair we taped it to a lens holder with no lens, shined a laser pointer at the hair, and measured the defraction lines that appeared on the screen behind the hair. In this process, there were sources of error that occured when we attempted to aim the laser at the hair, as well as when we traced the lines. When we aimed the laser we could not get it to consistently aim at the hair, and therefor had to hold it on the ring stand, and this caused inconsistency in the image produced. When we traced the lines we had difficulty keeping the stand in its position on the track, and the screen would move as we traced on it. This lab is a great example of how to measure the width of extremely small objects. Within a small percent of error we were able successfully calculate the width of a human hair, which is as small as 4 micrometers, in a high school lab. With higher technology available it could be possible to measure the size of almost any object on Earth, no matter how small.

=Lab: Atomic Spectra=

Objective:

To measure the wavelengths of light emitted from several different atoms with high accuracy, and then construct an electron energy level diagram.

Pre-Lab: > Helium: Red - 668, Yellow - 588, Green - 502, Blue-Green - 471, Blue - 447, Violet - 403, > Hydrogen: Red - 656, Yellow - 486, Green - 434, Violet - 471 > Mercury: Red - 690, Red-Orange - 615, Yellow - 575, Green - 545, Blue - 435, Indigo - 417, Violet - 405
 * 1) The objective is stated in the title. What is your hypothesis? (Attempt to answer the question, to the best of your knowledge.) In order to find the wavelengths of the visible spectrum of each element we must look at the elements through a diffraction grating which will show the visible light spectrum of each element clearly.
 * 2) What is the rationale for your hypothesis? (Provide detailed reasoning here. This may take the form of a list of what you already know about the topics, with a summary at the end.) We can then see how far the colors of the spectrum appear and with a known distance from the grating to the element we can then use the equation tanø=y/L where y is the fringe distance and L is the length from the grating to the element. When the angle is found, then using the equation a*sinø=m*λ, the experimental wavelength of the color that is seen can in turn be found.
 * 3) How do you think you might test this hypothesis? (Outline your methods and materials.) In order to test this hypothesis we will set
 * 4) Read through the procedure notes. Make any tables in order to organize your data and calculations.
 * 5) What is a continuous spectrum? A discrete spectrum? What type of light source produces each? A continuous spectrum is one that projects simply white light. There is no lines or bands because it emits every single wavelength and thus produces a white spectrum. A discrete spectrum is extremely different than a continuous spectrum because it is a spectrum of a specific integer number of intensities.
 * 6) Go to [] and record estimated wavelengths and colors for the emission lines for Hydrogen, Helium and Mercury.
 * 1) Go to [|http://astro.u-strasbg.fr/~koppen/discharge/] to see images of the emission spectra.

Hypothesis:

In order to find the wavelengths of the visible spectrum of each element we must look at the elements through a diffraction grating which will show the visible light spectrum of each element clearly. We can then see how far the colors of the spectrum appear and with a known distance from the grating to the element we can then use the equation tanø=y/L where y is the fringe distance and L is the length from the grating to the element. When the angle is found, then using the equation a*sinø=m*λ, the experimental wavelength of the color that is seen can in turn be found.

Methods and Materials:

Before beginning the lab, it is important to know the lines per millimeter of the diffraction grating. If it is not given, we have to find this through measurements in a mini-lab. We have to take the diffraction grating and tape it to an empty lens holder, and place it on an optics bench where it is marked at 0cm. Then place a screen on the other end of the optics bench, and place the screen at a set distance. Then, with a ring stand and clamp, shine a laser pointer of known wavelength through the diffraction grating so that multiple images appear. With a pencil and paper, trace where the multiple dots appear, and measure the distance of each point from the center image. Using this measurement and the set distance from the diffraction grating to the screen, we can find ø and use the equation d*sinø=m*(lambda) to solve for d, the number of lines per millimeter of the diffraction grating.

In this lab, we begin by making the classroom as dark as possible for when the lights are turned off. We did this by taping black sheets of construction paper on all of the windows in the classroom. Then we took the power supplies, one for each group, and had them face away from one another at the corners of the classroom. At the top of the power source we taped a meter stick with the 50cm mark at the middle. Then at the base of the power source we placed an optics bench with the highest cm mark nearest the power source. On this optics bench, at the point where the optics bench is marked as 0cm, we placed an empty lens holder, and taped a diffraction grating to the lens holder. Then we inserted a tube of a specific gas atom (hydrogen, helium, or mercury) into the power source, plugged it into a power outlet and turned it on. Then, with the lights off, a viewer looks through the diffraction grating and points to each color of the spectrum with a laser pointer. A second student records what the distance is from the center of the meter stick, as well as the corresponding color. Each different gas had different colors and a different amount that were visible. With this data we are able to calculate the wavelength of the colors which are visible through the diffraction grating using the equation d*sinø=m*(lambda) with the d calculated above and the ø measured from the diffraction grating to the power source.

Data: Sample Calculations: Analysis:


 * 1) Calculate the wavelengths of hydrogen, helium, and mercury and evaluate your results.
 * 2) Use these wavelengths of the emitted photons to draw an energy level diagram for each atom. This must include quantum numbers, the transitions, associated energies, and write the color of the observed line next to its transition on your energy level diagram.
 * 3) Determine the wavelength corresponding to the various points in the spectrum that were located on the continuous spectrum.
 * 4) You probably couldn’t see the violet lines of mercury. Using the actual values from the Internet (restate source), calculate the expected position of the lines. If possible, go back to the set-up to see if you can find them now that you know where to look. Describe your results.

Discussion Questions:

Conclusion: 