Lab Report #5 (Exp

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Report for Experiment #15 Geometric Optics Vaughn Montoya Lab Partner: Ricardo Macrron TA: Ji Tae 3/24/2023

Introduction Lenses that date back to 1000 years ago, were the first known lenses discovered by Viking ruins on the island of Gotland. In today’s world we live with optical devices such as CD, DVD, and blue ray players. Geometric optics refers to how light travels and relates to lenses and mirrors. This was the point of this lab to see how light travels through items we interact with and see every day such as glasses and mirrors. Under geometric optics it is assumed that light travels in a direct line which are known as rays. We used this to look at refraction and reflection. There are different types of mirrors, plane mirrors, spherical, and paraboloidal mirrors. These are used to investigate the concept of reflection. Plane mirrors in which a ray is reflected will be the same reflected back and the normal force will be perpendicular with the incidence and reflection angles being equal. Refraction is how light is altered upon entry into a transparent material. When looking at refraction we can use two formulas, the index fraction which is ratio of speed of light ( 3.00 x 10^8 m/s) which is highlighted in the following formula: n = c v Then the second equation is known as Snell’s law or the law of refraction which can be seen in the equation below: ࠵? ! ࠵?࠵?࠵?࠵? ! = ࠵? " ࠵?࠵?࠵?࠵? " Snell’s law allows light to move from a material to another and the equation above is used to manipulate and solve for the respective indices of fraction. Lenses allow for the transmission of light rays. When it comes to lenses in this lab, we looked at two, converging and diverging lenses. Converging rays refracted to a single focal point and diverging rays caused the rays to never cross paths. This lab looked at parallel light ray reflection on plane and spherical mirrors. We had to find the refractive index of a rhombic prism. Then we had to investigate refraction of parallel rays in convex and concave lens. The focal length had to be obtained using a thin lens using a form of bench optics. During Investigation 1, we examined the principles of ray tracing for concave and convex mirrors and lenses using both reflection and refraction. Then in Investigation 2 light was refracted through an acrylic trapezoid which looked at how the rays of light entered the trapezoid and exited the trapezoid at specific angles. In Investigation 3 focal length of a thin lens was looked at using an optic rail bench. The image was reflected on a metal screen through a lens and the dimeter of the refracted and original image were computed.

Investigation 1 The setup for Investigation 1 consisted of ray tracing with a concave mirror we used a triangular mirror that had both concave and convex sides during the Investigation along with using a PASCO light source. The room lights were switched off and the light source was adjusted to so that five rays came out. Our TA then gave out pieces of white paper so then we could trace it on the paper. The mirror and lenses, concave and convex were used and the focal points were determined. The table below highlights this: Focal Length, f (m) δf (m) do (m) Nominal Value (m) δNominal Value (m) Concave Mirror 0.060 0.005 0.158 0.063 0.003 Convex Mirror 0.068 0.015 0.166 0.063 0.003 Concave Lens 0.114 0.01 0.180 0.129 0.005 Convex Lens 0.142 0.15 0.14 0.129 0.005 We measured the focal length of concave/convex mirrors and lenses which were determined by measuring the distance between the focal point and the point where the incident rays converged or appeared. The error of the focal length was simply half the smallest increment. The focal length for the concave mirror was 0.060 m ± 0.005 m and the convex was 0.068 m ± 0.015 m. These values were compared to the actual, nominal values of the convex and concave mirror, 0.0630 m ± 0.003 m. The experiential values obtained were within range. Then the lens focal points were 0.114 m ± 0.01 m for the concave lens and 0.142 m ± 0.15m for the convex lens. The nominal value given by the manufacturer was 0.129 m ± 0.005 m and the experimental values are within error.

(Figure 1: Diagrams of Investigation 1) Investigation 2 The setup for this Investigation consisted of getting an acrylic trapezoid from the kit and placing it in front of the PASCO light source. IPL manual said to rotate the ray until we got an angle between 35 ° and 70 ° my TA just wanted us to get four different angles. The incident ray was then traced exiting the trapezoid and connected via ruler. Then the refracted and incident angle were measured with respect to the normal force utilizing a protractor. The table below highlights the data gathered for this Investigation: θ incident (degrees) θ refracted (degrees) Index of refraction (n) δn average n δn avg 33.0 22.0 1.454 0.03698 1.429 0.01383 38.0 28.0 1.311 0.02603 50.0 32.0 1.446 0.02280 55.0 33.0 1.504 0.02220 Snell’s law was used to calculate the Index of refraction which was the equation used in the introduction where we solved for n and kept in mind to convert to radians while solving. Then the error of n was found by using the following equation: ࠵?࠵? = ࠵? ࠵?࠵? ࠵?ℎ࠵? ࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?ℎ࠵? ࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? √࠵? In the denominator, N refers to the 4 because that’s how many angles we measured and in the numerator that standard deviation of the values was taken. Then the average was found by adding up the index of refraction values and dividing them by four which can be seen below: ࠵?࠵?࠵? ࠵? = ࠵? ! + ࠵? " + ࠵? # + ࠵? $ 4 Then the error of n average was found by using the following equation: ࠵?࠵? %&’ = @(࠵?࠵? ! ) " + (࠵?࠵? " ) " (࠵?࠵? # ) " (࠵?࠵? $ ) " 4 Where each δn was taken and 1 through 4 and squared and divided by 4. We compared the average index of refraction to the expected value during the Investigation. The average index found was 1.429 ± 0.01383 and compared to the actual value of acrylic, 1.49 which does not fall within uncertainty. This error could have been because the light source wasn’t powerful enough which made it difficult to trace the incident and refracted rays. This could simply be improved by getting a stronger light source.

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