radius of mth order dark fringe slit L-L0m sereen Figure 11: A side-view of the online simulation, defining the geometry used to analyze single-slit diffiaction pattems. The formula for the yorder dark fringe in single-slit diffaction is m =1 m = 3 m = 2 m2 = Dsine Equation 1 Where Dis the slit width. Notice that e can be found via Pythagorean's theorem from Figure 11. Figure 10. Procedure to measure the fringes from the online simulation. sine = Equation 2 • Notice at the top left of the diffraction image screen, there is a 10 mm scale. • Use this scale to estimate the radius of first dark fringe. • To do this, take a piece of paper and, within the simulation, place it against your computer screen to Here, y is the radius of the mt order dark fringe, as indicated at the right of Figure 11. Using Equation 2, find sin e for each of the dark fringe orders in Table 1. Enter these values into the third column of Table 1. Be sure to use consistent wnits for the lengths! mark the 10 mm distance. • From this, construct a homemade ruler with 5 mm, 10 mm, and 20 mm drawn on the paper. • Use this homemade calibrated ruler' to estimate the radius (from the center of the bright green circle to the center of the dark fringe). Enter the radius, y, estimate into Table 1, making sure to include proper wnits. • Continue measSuring the radii for dark firinge orders 2, 3, and 4. Enter them into Table 1. Try to do estimate your values within 1-2 mm accuracy. Using the data from each row in Table 1, together with Equation 1, estimate the slit diameter, D. Recall that ?. 511 nm. Enter the values for D into the last column of Table 1. Table 1: Data table for Activity 2, using ?, = 511 nm. Insert your work for one of your 'D' calculations here. Dark Fringe Order Radius of Dark Fringe, y sin e D. slit dianeter m=1 7mm m=2 14mm m=3 18mm m=4 22mm Q11. Find the average value of your four estimated slit diameters. If this is not roughly equal to the value specified in the experiment as the 'accepted' value of 0.1 mm, go back and check your work Ensure tha you are using consistent units for lengths. Consider a side-view of the slit and screen as shoyn in Figure 11. Notice that the slit to screen distance is 1.0 m.

A map suggests that Atlanta is 730. miles in a direction 5.00°north of east from Dallas. The same map shows that Chicagois 560. miles in a direction 21.0° west of north from Atlanta.Figure P1.68 shows the location of these three cities. Modelingthe Earth as flat, use this information to find the displacementfrom Dallas to Chicago.

Vector A = 7.4 i + 3.2 j.  Vector B = 3.7 i - 7.1 j. Calculate the angle between the two vectors in degrees.