PART 1: Index of Refraction for Rectangular Block In the first part of the experiment, you will determine the index of refraction of an acrylic block. The index of refraction will be determined from measured angles of incidence and refraction. Place the rectangular acrylic block on the graph paper on the following page and trace its outline. Place it aside. Select a normal line to the outline of the block's surface. The line should be approximately at the center of the block's face. With your protractor, draw a line of incidence to the same normal line, using angle 01 of 20.0, as shown in Figure 2. Label the angle carefully. Place the block in the previously traced outline. Using the laser pointer, shine the red light ray along the drawn line that forms a 20.0 angle of incidence. Looking at the block from above, observe the bending of the light ray in the block and its emergence on the other side. Trace the emerging ray with your ruler. Remove the block and connect the incident and emerging ray. Measure the angle of refraction 02 and record your data in Table Figure 2 1. Make sure you measure the angle the refracted ray makes with the normal line. Estimate the error of each angle of incidence and refraction based upon the precision of your protractor, for example, 10.5 or +1 Calculate the sine of each angle and record in Table 1. Repeat the experiment with three other angles of incidence, for example, 30.0, 40.0, and 50.0. The following equation (Eq. 4) may be used to estimate the uncertainty of each angle in radians (use the appropriate uncertainty from your protractor): Asin 0 = (0.50 X - . cos 0 [Eq. 4] 10. Construct a graph of sin 02 vs. sin 01. Record the slope of the graph and propagate the error. 11. Q1: What is the index of refraction of the acrylic block? 12. Q2: What is the speed of light in the acrylic material? 13. Q3: Calculate the critical angle at the acrylic-air interface. TABLE 1 X 4X AY 0 1 401 0 2 40 2 sin 01 A sin 0 sin 02 A sin 02 20.0 O. S O.5 0, 342 0.470 3 0.191 04943 3010 05 0.5 0.5 00 0.4350.276 0.484 40,0 0.5 185 05 0.643 0.385 0.312 0.494 500 0 5 20 05 0966 03 240.454 0.446PART 2: Index of Refraction of Water You will now measure the index of refraction of water, using a similar procedure as the previous part. This time you will use the semi-circular dish filled with water. The index of refraction will be determined from experimentally measured angles of incidence and refraction. 1. Place the semi-circular dish on the graph paper on the following page and trace its outline, as shown in Figure 3. Place it aside. 2. Select a normal line to the outline of the dish's surface. A The line should be approximately at the center of the straight edge. 3. Repeat the procedure from the previous part, shining the light ray incident on the flat surface with a pre-measured angle (01) that is clearly labeled on the diagram. Shine water the laser so the ray aligns with the angle of incidence you have drawn. air 4. The dish has a protractor on its bottom surface, so you may measure the angle or refraction (02) for the laser ray. 5. Estimate the error of each angle of incidence and refraction based upon the precision of your protractors, for Figure 3 example, 10.5 or +1. 5. Repeat the experiment with three other angles of incidence. Record your data in Table 2. 7. Construct a graph of sin 02 vs. sin 01. Record the slope of the graph and propagate the error. 8. Q4: What is the index of refraction of water? 9. Q5: What is the speed of light in water? 10. Q6: Explain why the refracted ray does not change direction when it re-enters air at Point A. 11. Q7: Calculate the critical angle at the water-air interface. TABLE 2 X AX y AY 0 1 401. 0 2 40 2 sin 01 A sin 01 sin 02 A sin 02 20 14.5 0.5 0.342 0.470 0.25'0 0.484 22.5 05 0.500 0. 433 0383 0.462 40 O.5 0.643 0.363 0.462 0.44 5100 26 O.S 10.266 0. 321 0.5%8 10.405\fPart 1 sin Q, sin Oz ne 0. 342 0. 191 1.79 0 500 0. 276 1.8 0. 64 3 0. 317 2.03 0. 766 0. 454 1. 69 Taking the average of n,, we get 1.8 1. 79 + 1. 8 + 2. 03 + 1.69 - 1 8 4 m2 = 1.8 Paut 2 sino , sen @ 2 0. 342 0. 250 10 36 0. 500 0. 383 1. 305 0 . 643 0. 462 1. 39 0 . 7 66 0. 58 1.32 Taking the average of n , we get 1.34 1. 36 + 1. 305 + 1 . 39 + 1. 32 - 1. 34 4 n2 = 1.34n, Sin 01 = n sino nz = Misino, sun Q 2 Taking refractive index of air , n , = 1.0003