Determining Focal Length of a Lens--Bessel Method

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Overview:

Suppose an object and screen are a fixed distance D apart. A converging lens located between the object and screen will form a real image on the screen at two distances whose separation is d and is given by:

Note that the above relationship is derived in the note [note4.pdf] which gives examples of using matrices in geometric optics.

Goal of this Experiment: The goal of this experiment is to determine the focal length of a lens by locating the two positions where a real image of the object is formed 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. The object to screen distance must be greater than four times the focal length of the lens being used. Record the distance between the target and the screen.
  2. Determine the two positions of the converging lens which yield a clear image of the target on the screen.
  3. 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 function of the form:

Questions:

  1. What is your estimate of the random and systematic errors in determining d and D ?
  2. What is the resulting error on your determination of the focal length ?