One way to measure the focal length of a lens is to take advantage of the concept of reciprocal magnification. For any object to image distance, there are two positions of the lens that will form an image (this assumes that the object to image distance is greater than 4f). The lens is moved until the image is formed at the desired location. For example, it could be focused on a screen. Then the lens is moved to the other position where the image is formed at the same location. The distance the lens was moved and the object to image distance is used to calculate the focal length. The figure below shows the experimental setup. The lens position one and lens position two show the two measurements that are made. The measured results are a=184.0 mm, b=816.0 mm, and c=1,000.0 mm. Please note that c is the same in both measurements because the distance from the object to the image is fixed. All distance measurements are made with respect to the object location.

a) Use the equation?=(D^2-L^2)/4Dto determine the focal length. D is the distance from the object to the image, and L is the distance from lens position 1 to lens position 2.

b) The object height, h1, is 5 mm. Show that the magnification for position 1 is the reciprocal of the magnification for position 2.

For parts c through f, the uncertainty in any distance measurement is 0.10 mm.

c) When focusing a lens, there is a small range of distances around the ideal focus where it is difficult to see any change. This means that there is some uncertainty about where the lens should be positioned. When the lens is in position 1, we can't tell the difference if the lens is within 0.26 mm of its ideal location. Once the lens location has been adjusted, distance a is measured, and the measurement has an additional uncertainty of 0.10 mm. What is the uncertainty in the value of a?

d) When the lens is in position 2, we can't tell the difference if the lens is within 0.02 mm of its ideal location. Once the lens has been adjusted, distance b is measured, and the measurement has an additional uncertainty of 0.10 mm. What is the uncertainty in the value of b?

e) What is the uncertainty in L?

f) D has an uncertainty of 0.10 mm. What is the uncertainty in the measured focal length?