( Ill) In the magnification method, the focal length / of
Chapter , Problem 109(choose chapter or problem)
( Ill) In the magnification method, the focal length / of aconverging lens is found by placing an object of knownsize at various locations in front of the lens and measuringthe resulting real-image distances d[ and their associatedmagnifications m (minus sign indicates that image isinverted). The data taken in such an experiment are givenhere:d{ (cm) 20 25 30 35 40m -0.43 -0.79 -1.14 -1.50 -1.89(a) Show analytically that a graph of m vs. d[ shouldproduce a straight line. What are the theoretically expectedvalues for the slope and the ^-intercept of this line? [Hint.d0 is not constant.] (b) Using the data above, graph m vs. d[and show that a straight line does indeed result. Use theslope of this line to determine the focal length of the lens.Does the ^-intercept of your plot have the expected value?(c) In performing such an experiment, one has the practicalproblem of locating the exact center of the lens since d[must be measured from this point. Imagine, instead, thatone measures the image distance d[ from the back surfaceof the lens, which is a distance from the lenss center.Then, d[ = d[ + t Show that, when implementing themagnification method in this fashion, a plot of m vs. d[ w illstill result in a straight line. How can / be determined fromthis straight line?
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