2.For Procedure 2 use the second equation, the distance and the average time squared to calculatethe average acceleration for each position. Compare these accelerations, are they equal? Howmuch do you trust your results? Discuss the answers in your conclusion.Graphs:1.Plot a graph of d vs. tavg2.Plot a graph of d vs tavg23.Discuss these graphs in your conclusion. Use the slope of the second graph to find the a cceleration, how does this acceleration compare to the average acceleration from Procedure 1?81

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FOCAL LENGTH OF A CONVERGING LENS(Adapted from “Advanced Physics with Vernier - Beyond Mechanics” Manual)Apparatus:SVernier dynamics system trackSVernier optics expansion kit containing:- light source- 20cm converging lens- screen.SRulerSLED lampObjective:Explore how lens characteristics and the position of the object affect the appearance, orientation andsize of real images. Determine the relationship between object distance, image distance, focal length and magnificationin real images produced by converging (bi-convex) lenses. Discussion:In this experiment we will have the opportunity to see the real images produced by a converging lensby projecting that image on a movable screen of an optical bench. See Fig. 2. Fig. 1 - Set-upFig. 2 - Sample Image Formation by a Converging Lens 83

Eq. 1Eq. 2Eq. 3The metric scale on the bench, will allow us to accurately determine object distances doand imagedistances di, providing us a means of verifying the lens equation:where fis the focal length of the lens. We will also be able to check the validity of the magnification relationship:where hoand hiare the heights of the object and image respectively.Eq. 1 can also be written as:Fig. 3 - Object and Image DistancesFig. 4 - Magnification84

To illustrate the basis for our graphical approach, let us set 1/diequal to y, 1/doequal to x, and 1/fequal to b, so that Eq. 3 becomes:y = -x + bEq. 4 which is clearly, the equation of a straight line. The slope of this line is equal to -1and its y-interceptbequals 1/f. If we plot y(that is, 1/di) against x(that is, 1/do), we should get a downward slopingstraight line that intercepts the y axis at b (that is, 1/f). Note that the x-intercept also equals 1/f. Wetherefore have a graphical method for determining the focal length of our converging lens.Procedure: 1.Attach the light source assembly on the track. Position it so that the pointer at the base is at the2cm mark and the light source faces the other end of the track. 2.Turn the light source wheel until the number “4" is visible in the opening. This will be the“object” for this experiment. Note that the height of the object hois 2.0cm.3.Place the 20cm bi-convex lens at the 35cm mark. 4.Place the screen at the 120cm mark of the track so that the light from the light source passesthrough the lens and strikes the screen.