Group4_8_ch24

=Lab: Polarization= toc Group: Ryan Listro, Allison Irwin, and Rebecca Rabin Date: 12/19/11

PURPOSE What is the relationship between intensity and angle of polarization?

HYPOTHESIS Light intensity is inversely proportional to the square of the distance from a point light source and the intensity of the light transmitted through two polarizers depends on the square of the cosine of the angle between the axes of the two polarizers. This can be proven using Malus' Law equation,.

SETUP/METHODS The materials used include the following: an optics bench used for mounting various lenses, eyepieces, and light sources; point light sources used to cast light through the polarizers; 2 polarizers used for experimenting with the light's intensity in context with the angle of polarization; a photometer used to display the different intensities of each light source; and 3 brackets used for attaching the light attachments to the optics bench.

DATA

Class Data

CALCULATIONS
 * Using trial averages

DISCUSSION QUESTIONS 1. How do polarizing filters work? Polarizing filters have the capability of blocking one of the two planes of vibration of an electromagnetic wave. When a polarizing filter is put into use, it takes out 50% of the vibrations or intensity and thus the unpolarized light becomes less bright. 2. How is the polarizing filter different from the neutral density filter? While both the polarizing and neutral density filters have similar purposes they work very differently. As stated in question 1 a polarizing filter blocks one of the planes of vibration, however, a neutral density filter simply has a certain percentage of the filter blocked by black spots. The black spots prevent 100% of light getting through the filter. The amount of light allowed through depends on how much of the filter is covered by black spots. 3. How were your results? Our results were extremely accurate. While the 50 percent of transmission had absolutely zero error, our 75 and 25 percent of transmission had 6.429% and 6.00% error, respectively. When compared to the rest of the class, our 50 percent was closest to the theoretical, our 25 percent was second closest, and our 75 percent was third closest. So, overall, our results were very precise. 4. Discuss sources of experimental error. Possible sources of error could have come from human inaccuracy. It was extremely difficult to read the angles projected on the filter as well as knowing exactly when each side was exactly the same brightness. Error could have also come from light within the classroom. The room was not completely darkened and could have thrown off our observations.

=Lab: Snell's Law= Group: Allison Irwin, Rebecca Rabin, Ryan Listro Date: January 5, 2012

Purpose: To derive Snell's Law experimentally, to determine the index of refraction experimentally, and to compare the index of refraction for acrylic and water.

Hypothesis: According to Snell's Law, we believe that the index of refraction for acrylic and water will be equal to the sin of the incident angle divided by the sin of the refracted angle. Materials: To perform this experiment, some materials are needed. Two key materials include an acrylic block and a water lens filled with water, which will serve as the mediums in which light will enter and refract. This brings up another material– the light source, which will be used to shine on both the block and the lens. The final two materials needed are a ruler and a protractor, both used to aid in finding the refracted angle.

Procedure: Place the rectangular block on the lab table, on top of the template provided for you. Rotate the light source along the incident rays drawn on the template. For each, clearly mark the position where the light exits the block, but do not trace the ray that you see on the paper. The exit point is all that matters. After you mark each angle, remove the rectangular block and draw a line connecting the point where the light entered to the dot you just drew. Repeat this process for the plastic semicircular “lens” filled with water. Once all data is collected, with a protractor, measure the angle inside the block. This is the refracted angle. To determine the index of refraction for each block, create a graph of sin of the incident angle versus the sin of the refracted angle. The slope of this graph will be the index of refraction for each different medium.

Data: Group 4 Data: Class Data: (Group 1 Data is from Erica Levine, Bret Pontillo, and Steven Thorwarth, Group 2 Data is from Sam Fihma, Chris Hallowell, and Phil Litmanov, and Group 3 Data is from Ross Dember, Eric Solomon, and Richie Johnson) Calculations: Analysis:

Discussion Questions: 1. State as quantitatively as possible the precision of your value for //n//, the index of refraction. The precision of our data is extremely accurate due to the fact that our percent errors are both below 2%. For acrylic, our experimental n was 1.491, which, when compared to the theoretical of 1.49, is only a 1.53% error. For water, our experimental n was 1.356, which, when compared to the theoretical of 1.333, is only a 1.62% error.

2. State how your data for the acrylic prism are evidence for the validity of Snell’s law. Using an acrylic prism, we were able to test Snell's Law. By shining a light into the prism at various angles, we were able to measure and record the corresponding refracted angles. After this, we were able find the index of refraction inside the prism by plotting a graph of the sin of angle of incidence versus the sin of angle of refraction. We know the slope of this graph is the index of refraction because of Snell's Law, sin(angle of incidence)=(nr/ni)sin(angle of refraction). In this equation, ni is the index of refraction of air, which is 1; so, the equation can be rewritten as sin(angle of incidence)=nr sin(angle of refraction). In our graph, sin(angle of incidence) is the y value, while the sin(angle of refraction) is the x value. When compared to the equation of a linear graph, this would leave nr as the slope, which, in the end, was 1.491. When compared to the theoretical value of 1.49, we can prove the truth and validity of Snell's Law because of the small amount of error.

3. Using the value of //n// determined for the acrylic block, find the speed of light in the prism. 4. Inside a prism the wavelength of the light must change as well as the speed. Is a given wavelength longer or shorter inside the prism? Consider specifically light whose wavelength is 500 nm in air. What is the wavelength of this light inside the prism? Inside the prism, the wavelength is shorter than its original 500 nm. Because of the equation n=wavelength (vacuum)/ wavelength (medium), the wavelength of the medium would equal the original wavelength, 500, divided by the index of refraction. Since the index of refraction is greater than one, the wavelength in the medium will be shorter. After calculations, the wavelength inside the prism is 340.72 nm.

Conclusion: With our experiment, we concluded that the index of refraction of acrylic was 1.468 and the index of refraction of water was 1.365. This was found using the Snell’s Law equation and the following calculation: These results thus prove our hypothesis correct. The index of refraction of both acrylic and water were in fact the sin of the incident angle divided by the sin of the refracted angle.

Our results were also extremely accurate. The theoretical index of refraction for acrylic is 1.49 while our experimental index of refraction was 1.468. The theoretical index of refraction for water is 1.33 while our experimental index of refraction was 1.356. Using these values we concluded that the percent error for our experiments on acrylic and water were 1.53% and 1.65% respectively. This error could have been entirely from human mistake. While performing the experiment it is very possible that the rectangular block and/or the plastic semicircular “lens” with water could have moved on the paper between taking the markings of each angle. This would have thrown off the angle from the normal line, leaving inaccurate results. Error could have also come from incorrect measurements taken when using the protractor. This too would throw off the final results.

In order to address this error, it would have been vital to use a more stable set up and accurate technology to measure the angles precisely. If the objects were secured there would have been no chance of any motion. In addition, we could have measured the angles incorrectly. With a device more advanced than a protractor, our results would have a greater chance of accuracy. Fiber optics is also entirely based on Snell’s Law. This is useful to our society because the index of refraction in certain materials allow the transmission of light signals over long distances. Unlike other methods of transmission, materials used in fiber optics do not heat and therefore do not use energy.

=Lab: Lenses= Group: Rebecca Rabin, Ryan Listro, Allison Irwin Date: 1/12/2012

Purpose: To precisely determine the focal length of a thin lens. To verify the image characteristics formed when objects are placed at varying distances from a lens. To validate the thin lens equation.

Hypothesis: Part A: According to the thin lens equation, we can calculate the focal length: Part B: To verify the thin lens equation, and that our focal length was correct from Part A we should observe the following during Part B:
 * 1) A real, inverted image when the object is placed beyond 2F, at 2F, and between 2F and F.
 * 2) No image at F.
 * 3) No image between F and V because the image is virtual (it will not be projected on the screen).

Procedure: Materials To ensure successful completion of this activity, several materials are necessary and important. A light source, which will be used as the "object", a convex lens, and a screen are all to be placed on an optics bench in that respective order. This setup can is explained in detail and shown below. It is convenient to have an optics bench with a measurements along the side however this is not necessary.

Methods To begin this experiment, place the optics bench on a flat surface in close proximity to a power outlet. Attach both the screen and the light source (the object) to opposite sides of the optics bench and position the convex lens in between. The order of these three objects will NOT change throughout the remainder of the experiment. This setup is displayed accurately through the diagram below. Also shown is the image distance (di) which can be found by measuring the distance between the screen (if the image is projected) and the lens, as well as the object distance (do) which can be found by measuring the distance between the light source (object) and the lens. When the setup is complete, plugging the light source into an outlet will allow experimenting to begin.

Although a light may be projected from the light source (the object) it is important to note that an image will not necessarily appear on the screen with all variations of image distance and object distance. To retrieve an image, slide the lens back and fourth until a position is found that indicates a clear, focused image on the screen. It is important to accurately measure the image distance and object distance because these results will be used as trial one. Moving both the screen and the light source (the object) to new locations will allow for new image distances and object distances. It is vital to remember that although the positions of the screen and the light source (the object) are changing, the order in which the three objects are placed does NOT change. This process should be repeated until ten different variations of distances are found that project a clear, focused image on the screen.

To complete the second part of the experiment, an identical setup is to be used. After turning the light source, a picture should be seen on the light source. This is the object and measuring the size of the arrow will give the height of the object size. The same process is used as above however, each trial is indicated as beyond 2F, at 2F, between F and 2F, at F, and between F and V. F is the focal length which is constant for each lens and can be indicated on the lens. V is the vertex which simply represents the location of the lens. Finding clear and focused images at each distance or distance range may not be possible. For these observations simply indicate "none". For those images that are able to be produced the size of the arrow will give the height of the image size. It is important to note that the image may be inverted, for all cases like this, the height is a negative number

Data and Observations: Calculations: Graph: Lens 1: Irwin, Rabin, Listro (F=100 mm) Lens 2: Pontillo, Thorwarth, Levine (F=250 mm) Lens 3: Johnson, Solomon, Dember (F=200 mm) Lens 4: Fihma, Hallowell, Litmanov (F=500 mm)

Discussion Questions: 1. How do the slopes of the various lenses compare? How can you tell which lens has the bigger focal length using the graph? The slopes of the various lenses are approximately equal to each. The lens with the largest x and y intercept will have the smallest focal length and the lens with the smallest x and y intercept will have the largest focal length. 2. Are the images real or virtual? How do you know? The images are real. We know this because the image is on the opposite side of the mirror. In addition, all images seen in this experiment are inverted and inverted images are always real. 3. In all trials, were the images formed by the lens erect or inverted? Explain why. All images were seen were inverted because they were real images. We did produce virtual and upright images however, due to lab limitations we were unable to see those images. 4. Explain why, for a given screen–object distance, there are two positions where the image is in focus. There are two positions where the image is in focus because of the anatomy of a convex lens. Both sides 5. How did the image distance change as the object was brought closer to the lens? As the object was brought closer to the lens, the image distance increased. 6. How did the image height change as the object was brought closer to the lens? As the object was brought closer to the lens, the image height 7. Compare and contrast characteristics and images of lenses and mirrors. Convex mirrors and concave lens are very similar while concave mirrors and convex lens are very similar. When using a concave lens or a convex mirror, the image characteristics are always virtual, upright, and reduced in size. When using a convex lens and a concave mirror, the image characteristics can either be enlarged or reduced, real or virtual, and upright or inverted. 8. Explain your results for trials 4 and 5 in Part B. In trial 4 of part B, no image was shown because the object was located at the focal point. In trial 4 of part B the image was located on the same side of the lens as the object and therefore could not be seen. 9. For trial 5 in Part B, calculate the theoretical di, hi, and M. Show your work clearly. 1/di=1/f-1/do 1/di=1/10-1/5 di=-10 cm

hi/ho=-di/do hi=(-10/5)(3) hi=-6cm

M=hi/ho M=-6/3 M=-2 10. Can you think of a way to project the image produced by an object between F and V onto a screen? It is not possible to project the image between F and V because said image is virtual. This means that light rays never truly intersect at a point.

Conclusion: Our hypothesis for Part A was correct. Using the thin lens equation, we found our focal length to be 96.9181mm. The actual focal length is 100mm. This is 3.08% error. This error most likely occurred when we took our distance measurements. Each time we had to measure object distance and image distance there was a chance for human error. Additionally, we had to manually focus the projected image. Whether or not the image was focused was based on our individual judgment. For example, if we were off by a single millimeter when we measured object distance, when we measured image distance, and when we focused the image, this would account for our 3% error. While we were very careful to measure precisely, there is still likely to be human error. The best way to fix the error would to have a device to more accurately measure the distances. Also, some way of perfectly focusing the image would be necessary. Our hypothesis for Part B was also correct. There was no image when the object was placed at F or between F and V. Using the object distance and image distance, we calculated the magnification for the other three trials. Our percent differences for these trials were 7.2539%, 6.0700%, and 3.6364%. This difference is most likely because our focal length from Part A was 3.08% incorrect. Also, we had to further measurements in part B, contributing further error. We could have fixed this error by again having a more precise way of measuring the distances, eliminating the human error. We also could have used the lens’s real focal length of 100mm for part B, rather than our experimental value of 96.191mm. After the lab, we found another way to confirm the thin lens equation. By holding the setup up by the window, we used the objects outside as our object. Because the distance of the outside objects was very big, we considered it to be infinity. In order to focus the image on the screen, we moved out lens to 100mm. This also validates the thin lens equation.  A real life application for this lab would be when using a projector. For a teacher to properly focus the image they can use the dial to adjust the object distance. They can also move the projector closer to or further from the screen, changing the image distance.