PHYS222_Lab7

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Dec 6, 2023

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Name: Taylor Totorp Email: ttotorp@vols.utk.edu Laboratory 7 Report Goal: This lab focuses on how light will interact when at a boundary of two different indices of refraction in two transparent media. It will work with how to find the reflected light beam, transmitted light beam, and the direction of propagation. Exploration 1: a) • The graph above looks very similar to the one provided in the lab. • Based on the graph of my results, the laser light should be s-polarized. The trend of the data of my graph is most similar to the s-polarized. 0 5 10 15 20 25 30 35 40 45 50 0 10 20 30 40 50 Relected Intensity R (%) Angle of Refraction (θt deg) Reflected Intensity vs. Angle of Refraction

• The plot of sinθ i versus sinθ t looks like a straight line. • The slope of the trendline is 1.341 • Given Snell’s law, the slope is expected to be 1.333, which is very close to the slope that I found in my experiment. b) To determine the index of refractions of two mystery materials A and B, I would run two similar experiments to the previous one above. First, I would change the bottom material to a mystery material A with the top as air. Running the same experiment as above measuring the angle of refraction and the reflected intensity. I would, then, repeat this same process with a different mystery material B on bottom. Creating another graph for each to find the plot of sinθ i versus sinθ t , this plot’s slope will be the n value for each material. n A = 2.3916 and n B = 1.3909 c) For the refracted ray to bend away from the normal there is a higher refractive index on top with water and a lower refractive index on bottom with air. y = 1.341x - 0.0054 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 sin(theta(i)) sin(theta(t)) sinθ i versus sinθ t

d) The laser beam after total internal reflections moves parallel to the incident beam but in the opposite direction. e) • The reflection and refraction of light is color dependent, because when switching to white light the only color that still followed the refraction path above was red. The rest fan out in a different angle. • The triangle splits the colors best out of all of the shapes but pairing the triangle with a circle after really accentuates that color split. • I chose a triangle paired with a circle to show that rainbow.

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Exploration 2: case R (m) f x o x i 1/x 0 + 1/x i 1/f M image real? image upright? concave mirror, real image: |hi| > |ho| 10 5 4 -33.70 0 0 7.747126 yes inverted concave mirror, real image: |hi| < |ho| 8 4 4 49 0 0 -11.30805 yes inverted concave mirror, virtual image 12 6 4 -16 0 0 3.648276 no upright convex mirror -10 -5 4 -2.3 -0 -0 0.535632 no upright • My results show that as the R increases the hi also increases. This also showed that the image is inverted when it is a real image and upright when it is a virtual image. • The main situation I can think of for mirrors producing the images that we are exploring in cases 1-4 would be your eyes and contacts, as they have roughly the same shape and do the same work as we looked at before. Experiment: w d θ air deg θ air rad cos 2 θ air sin 2 θ air d/(w sin θ air ) (1 - d/(w sin θ air )) 2 n 2 n 2.8 0.25 347.8 6.07026 0.9553 0.04466 -0.42250467 1.606591798 0.578557 0.760629 2.8 0.5 337.7 5.89398 0.856 0.14399 -0.47059831 0.221462772 2.342355 1.530475 2.8 0.75 328.2 5.72817 0.7223 0.27768 -0.50831046 0.028708836 2.357501 1.535415 2.8 1 319.4 5.57458 0.5765 0.42351 -0.54879688 0 1.361236 1.16672 • No, it seems that the two middle measurements seem to reasonably agree with each other, but the first and last measurements are below those measurements a bit. • I would suspect that the measurements at d = 0.5 and 1 would be more accurate, because these measurements were made on the tick marks where the d = 0.25 and 0.75 measurements were made at the estimated half between tick marks. • Given these measurements, I would conclude that the index of refraction of the glass block is 1.24831 ± 0.36812 Reflection: In this lab, there were two explorations into how reflections and refractions produce light based on the angles and colors. and an experiment after. Exploration 1 focused on finding if our experimental data was close to expected results, then we used this method to find other refraction indexes and other designs with prism refraction. In the first part the slope of the trendline of the experiment was 1.341, which was extremely close to expected slope of 1.33. Some potential reasoning as to the difference would be that the angles of refraction were being measured by the

human eye and there is always possibility for error on readings. Using that basis, it can then be found that n A = 2.3916 and n B = 1.3909. The prism experiments find that colors are refracted at different angles for each of them. Exploration 2 focused on the measurement of refraction images at different angles. In this exploration, it was concluded that as the R increases the hi also increases and the image is inverted when it is a real image and upright when it is a virtual image. The experiment focused on combining all the previous practice and knowledge on the refraction of light to measure the index of refraction of the glass block in the experiment. It was found that the index of refraction of the glass block was 1.24831 ± 0.36812. In this experiment there seemed to be a decent amount of error, which is likely due to the fact that some measurements were taken at the visual estimate of what was the middle of the tick marks.

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