Phys 132 Lab 8

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University of Illinois, Chicago *

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132

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Physics

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Apr 3, 2024

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UIC Physics Department Physics 132 Experiment #8 Physics 132 - Lab #8: Geometrical Optics (Experimental Procedure and Data Analysis) This part of the lab must be completed entirely independently of your lab partner(s) or other students. Make sure that you avoid unauthorized collaboration and plagiarism. All suspected violations of the Standards of Conduct will be referred to Student Judicial Affairs. Lab Section (Day & Time): Fvidor 10 awn Name_ Station #: Part 1. Color Addition Figure 2 In the first part of the lab we will discover the results of mixing b* red, green and blue light in different combinations with the tools shown in Figure 2. 1.1. Turn the wheel on the light source to select the red, green, and blue color bars. 1.2. Place the convex length near front of the light source, so it focuses the rays and causes them to cross. 1.3 Move the screen to the focal point. Question 1: What color appears on the screen at this crossing point? _Whire 1.4. Now block the red ray with a pencil. Question 2: What color results from adding green and blue light? owe 1.5. Now block the green ray with a pencil. Question 3: What color results from adding red and blue light? MOVWIE /[ ved ouxrer vivn 1.6. Now block the blue ray with a pencil. Question 4: What color results from adding red and green light? Ne ow / 0¥ oNnge ouYrer vien Exp. #8 Page 4 of 7

UIC Physics Department Physics 132 Experiment #8 Part 2. Law of Reflection and Snell’s Law In the second part of the lab we verify the Law of Reflection and Snell's Law (or the Law of Refraction) with the materials shown in Figure 3. To begin, 2.1. Set the semi-circular acrylic block on the Ray Table as shown in Figure 3(top). 2.2. Rotate the knob on the front of the Versatile Light Source until one light ray emerges and arrange it so it perpendicularly crosses the at side of the center of the acrylic block. You can arrange it to align with the “Normal" arrow on the Ray Table (see Figure 3(bottom). 2.3. Now rotate the Ray Table such that the ray still crosses the center of the lens, but is no longer orthogonal, as in Figure 4. You should see transmitted and reflected rays. 2.4. Using the angle markings on the Ray Table, measure and record 6, in Table 1 and 6, in Table 2 along with that of the incident ray, 6;, for the incident angles, 6;. between 10° and 80°. 2.5. Estimate a reasonable uncertainty for these angles, considering the technique used to construct and measure them and record its values in Table 1. incoming reflected light ray Table 1 light ray 6; Uncertainty 0, Uncertainty (in degrees) for 6; (in degrees) for 6, 10 1 10 + | 20 20 30 %0 40 | 4o 50 50 60 Lo | 70 70 | 80 V) 20 v Exp. #8 Page 5 of 7

UIC Physics Department Physics 132 Experiment #8 Question 5: Are the incident angles, ;, Table 2 and reflected angles, 6,, equal within | 0 sin 6, _ O sin 6, stated uncertainty? in degrees) ' (in degrees) MeS ey Ok equa) 10 0. \1306 =7 01218 Lo Broked uncertainity, 20 0.3420 | - 02419 30 0.4999 2.) 0.%353% 40 0. 6427 2.¢ 0.43%3 2.6. In Excel, plot 6; vs. 6, graph. Then 50 0.7651 3\ 06.351%0 use LINEST( to find the slqpe_, y- 60 0. 8654 =2 0.5%77 intercept and its standard deviations » and record its values below. 70 0-929( Ho O.lby27 80 0.9%48 H 2 0 .661° Slope, % = | + g.Mmot? Intercept = 0 + H.04 X\~ Question 6: What would you expect for the values of the slope and intercept? Why? What were the main errors in performing this experiment? | wou\d ¢ pect e <\o pe o e ] ond fne inrercepy A0 Voo O .be conse boxn e B¢ and Gr are tne egual within Shoted Onceriainity, Sowae Qa:xa(sa,;\mc,ud&_ﬂgma@,fioo..“e&,w,m 0 aOVe\y vead W ompers. 2.7. Find sin 6; and sin 6, for the 6; vs. 6, values listed in Table 2. In Excel, plot the sin 8; vs. sin 6, graph and then use LINEST() to find the slope, y-intercept and its standard deviations and record its values below. Slope, sz* = .50/ 4+ p.02013 Intercept= -0-©17] '+ 0.0097 t Question 7: Does your measured index of refraction for acrylic agree with the accepted value of approximately 1.49 within error? Dlscuss the main sources of error in determining the index of refraction. N e My woswec\ w2 x of yefraction Qgrees X itnive acce preol Veilup. Yecadse \ gox 15O and tne acce pred valse s |49 . T waain SOVN(L ofF oY or 15 eSXivhon ng A\ &e becavse Uwoes VZXU v‘/\Ql‘/Jk‘; Yo ¥\ ey volue e W9 YOy wyon on . TTne Coy oNer\apped (-2 AR LS . Exp. #8 Page 6 of 7

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UIC Physics Department Physics 132 Experiment #8 Part 3. Total Internal Reflection and Critical Angle ) Figure 5 In the previous part, we found 8; > 6, as the light passed from air to acrylic (Snell's Law guaranteed this because /mair < macrylic). Total internal reflection may only occur when light passes from a medium with a higher index of refraction to one with a lower (n;> n¢). In this experiment, we want to setup a scenario in which light passes from acrylic to air. Figure 5 shows a schematic for how we can accomplish this. refracted 3.1. Begin with the ray of light from the Versatile Light Source orthogonally penetrating the curved portion of the D-shaped acrylic block along the "Normal" line that is transcribed on the Ray Table. You should see the ray of light emerge perpendicularly to the at surface of the acrylic along the opposite side's “Normal” tracing. incoming light ray 3.2. Next begin rotating the Ray Table. In doing so, you should notice the emerging ray of light from the acrylic's at side begins to bend. Though the effect is initially subtle, eventually you should reach an angle where the refracted light is now at 8, = 90°. This incident angle has reached the critical angle 6, - the point beyond which we have total internal reflection, and no refracted light escapes from the acrylic. 3.3. Measure the angle 6, at which the total internal reflection occurs. Use Eq. (5) to determine the index of refraction for the acrylic block. 3.4. Estimate the uncertainties for 8, and Zacrylic and record the 8., macryiic and its uncertainties below. BC = Hl - - L SR = Macrylic = \-’ I’I -+ 0O RO 2D Question 8: Does the nacrylic value agree with your findings in step 2.7 and with the accepted value within error? Discuss the main sources of error in measuring the index of refraction in this section. “See_ Noawe A Ve Aol OgeR weixa e findinas in pep 2.7 WDLOTE Nowryric 15 LY add fov sxeyp 2.7 0 gek .S EVAYIVIRLS (oW Q\\rg_ﬂ,«vuﬂ AOse (V) Vole £30€C10l\y APyl Yalain 9 R oleepted ual e OC exvor in actOuNt. e monn SOV OF erfor was Mayx B wos Novd o +erl winzre, sne Lignt vay Shopped. [+ was hard te distivguish \Vetieen Whor yale 1= 43" dne gnkvay was . *Parts of this lab manual are adopted from Optics I: Reflection, Refraction, and Lens Equation experiment manual developed by Department of Physics, Columbia University, NY (https://physics.columbia.edu). Exp. #8 Page 7 of 7

B Addition 8l E | F .6 H [ Part 2: Law of Reflection Table 1 6i s_6i or s _Or indegrees | indegrees |indegrees| indegrees 10 10 20 20 30 30 40 40 - 50 50 60 60 70 70 80 80 1 -7.1054E-15 8.1079E-17| 4.0943E-15| 1| 5.25453E-15| 1.5212E+32 6] 4200 1.65661E-28 Bivs. Or L] ® . . é ® Seriesl 40 50 60 70 20 30 12000 1.0000 03000 0.6000 sin(81) 04000 02000 0.0000 L M N 0 Part 2: Law of Refraction Table 2 6i sin(6i) ot sin(Bt) in degrees in degrees 10 0.1736 7 0.1218 20 0.3420 14 0.2419 30 0.4999 21 0.3583 40 0.6427 26 0.4383 50 0.7659 31 0.5150 60 0.8659 36 0.5877 70 0.9396 40 0.6427 80 0.9848 42 0.6690 1.49665 -0.01695492 0.02018| 0.009743712 0.99891| 0.010442046 5500.35 6 | 0.59974 0.000654218 sin(0i) vs. sin(6t) @ Seriesl 0.0000 0.1000 02000 03000 0.4000 0.5000 06000 0.7000 0.3000 sin{Bt)

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