Lab 8: Focal Length of Converging Lens Purpose/objective: In this activity you can investigate the relation between object distance, image distance and focal length of a converging lens. Equipment needed: 1. Computer 2. Paper, Pencil 3. Optic bench and accessories, two converging lenses, an illuminated object and a screen. (Here you will use this You Tube video to get data for object distance and image distance) https://www.youtube.com/watch?v=Xbqtj54b3fI Theory: Light rays that are parallel to the axis of a lens, after passing through the lens, converge to a point on the axis on the other side of the lens. This point is called the principal focus (F) of the lens. The distance between the center of the lens and the principal focus is called the focal length (f) of the lens. If you imagine a sphere with one side of the lens as part of it, the center of that sphere is called the center of curvature C of the lens. The distance between the center of curvature and the center of the lens is called the radius of curvature R of the lens. Notice that, because of the symmetry of the lens, it has two principal focii and two centers of curvature.

When an object is placed between the principal focus and the center of curvature, a real, enlarged and upside-down image is formed beyond C on the other side of the lens. The distance between the object and the lens is called U and the distance between the image and the lens is called V. If f is the focal length of the lens, then a relation between f, U and V can be written as Procedure: 1. Measure (write the data from YouTube video, which is provided) the V values for five different values of U as demonstrated in the video. https://www.youtube.com/watch?v=Xbqtj54b3fI Table1. Trials U (cm) V (cm) 1/U (cm-1) 1/V (cm-1) 1/f=1/U+1/V f (cm) 1 2 3 4 5 Average Focal length for the data: c F F c upside down image object u v Fig. 2 Object distance is u and the image distance is v 1 1 1 U V f

2. Draw a graph of 1/ V (in Y-axis) vs 1/U (in X-axis) as follows. (you can use excel to draw the graph) 3. Attach the graph (make sure that 1/V is on Y-axis and 1/U is on X-axis.) 4. By using linear trend line using excel and using the display equation option, write the straight-line equation. 5. What is the slope and Y-Intercept? 6. Using Y-Intercept, which is equal to 1/V at 1/U=0. That means when the object is at infinity. In this situation, lens equation, 1/U+1/V=1/f, becomes 0+1/V=1/f and therefore 1/V=1/f (you do not need to show any work for it -it is just an information for you) 7. Focal length of the lens, f= Y-Intercept=

8. Compare f obtained from (E, above) with average value of f obtained from table 1. Calculations/Checking your understanding 1. When a flower petal is 4.0 cm in front of a converging lens, the inverted image is half the height of the petal. What is the focal length of this lens? Show your work: 2. A statue that is 10.4 cm tall is placed 4.8 cm in front of a concave lens. The image is 4.0 cm from the lens. How tall is the image? Answer: 8.7cm Show your work: 3. A cell phone is placed 40 cm in front of a converging lens with a focal length of magnitude 20 cm. How far is the image of this phone from the lens? Show your work: Summary and Conclusions: