# Lab 12 Focal Length of a Converging Lens

Question Lab 12 Focal Length of a Converging Lens 1. Objective: To measure the focal length of a converging lens. 2. Equipment: Optic bench and accessories two converging lenses an illuminated object and a screen. 3. 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 ? of the lens. The distance between the center of curvature and the center of the lens is called the radius of curvature ? 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 3. Procedure: (i) Measure the rough focal length of lens 1 by focussing the image of a distance object on a screen and measuring the distance between the screen and the lens. Record this as the approximate focal length (f?) of the lens. Keep the lens at a distance (f?+2)cm in front of the lit object and move the screen to obtain a clear image. Measure and record U and V as follows U (cm) V (cm) 1/U 1/V Draw (i) a graph of 1/U against 1/ V as follows: The graph cuts the x-axis at A and the y-axis at B. At A 1/V = 0 and therefore 1/U = 1/f or U = f The reciprocal of OA will give a value of f. Similarly the reciprocal of OB gives another value for f. Find the average of the two f values. (ii) Draw a graph of U against V as follows: Draw a line making 45 o with the x-axis to cut the graph at A. Draw AB. OAB is an isosceles triangle and therefore OB = OA. This means that point A corresponds to U = V. At point A the equation 1/U + 1/V = 1/f becomes 2/U = 1/f or U = 2f. therefore distance OB = 2f. Similarly OC = 2f. Obtain the average value of f from these two measurements. (ii) Keep the screen in front of the object so that the distance between them is more than 4 times the rough focal length of the lens. Record this distance as D. Keep the lens in between the object and screen and move its position to obtain a diminished clear image on the screen. Mark the position of the lens as A. Now move the lens so that a magnified image is formed on the screen. Mark the position of the lens as B. Measure the distance AB and call it d. The focal length f of the lens is related to D and d as follows: Do this experiment for 5 different values of D and each time measure the value of d. Tabulate your data as follows: D (cm) d (cm) D 2 ? d 2 Use the data values in the table above to draw an appropriate graph and obtain the value of f from the graph. Obtain the average of the three f values you obtained and calculate the percentage error. Repeat the experiment using a second lens. 5. Questions 1. Describe two applications where lenses are used. What does the lens do in each of these cases. 2. Draw a diagram showing how a camera lens forms an image of a distant object on the film. Explain what is done to obtain clear pictures of far and near objects using a camera. 3. How is an eye similar to a camera? What mechanism in the eye helps us to see far and near objects clearly? Draw diagrams to illustrate. 4. What is meant by power of a lens? How is it determined?

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