Determining Focal Length of a Lens--Conjugate Foci Method

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Overview:

Suppose a converging lens is placed between an object and a screen, and is positioned so that a sharp image of the object appears on the screen. The distance between the object and the lens, the image and then lens, and the focal length of the lens are related by:

where f is the focal length of the lens, p is the distance between the object and the lens (object distance), and i is the distance between the image and the lens (image distance).

Goal of this Experiment: The goal of this experiment is to determine the focal length of a lens by positioning the lens between an object and a screen so that a sharp image of the object appears on the screen. A schematic of the lab set-up is shown below.

Suggested Procedures:

 

  1. Set up the apparatus as shown above. The crossed arrow target will be used as the "object," and its image will be projected onto the screen.
  2. Position the converging lens so that a sharp image of the target appears on the screen.
  3. Record the object and image distances.
  4. Repeat the procedure with various target to screen distances.

Sample Data:

The plot below shows data taken with this set-up of the experiment. The data displayed here were fit to a straight line. The x- and y- intercepts of the straight line yield 1/f.

Questions:

  1. What is your estimate of the error in the measurement of the object distance and the image distance?
  2. Verify experimentally that the minimum distance between the object and real image formed by a converging lens of focal length f is 4f. Also - prove this in your lab writeup.