Question

design an experiment to measure the effects of chromatic aberration? Just a simple procedure, thanks.

Answer 1

Chromatic aberration in lenses is an important concept in practice, but one that is not frequently studied in introductory courses, particularly in introductory labs. An addition to the typical lenses lab is presented, in which chromatic aberration can be easily measured using the standard equipment used by students in studying image formation. The qualitative and quantitative results should be well within the abilities of most students in these courses.

  

  

  

Typically, in the second semester of the introductory physics sequence, one or more lab exercises are done in optics, including finding the focal length of a lens. A standard apparatus uses an incandescent light source with a ground glass diffusing screen, fronted by an �object�, such as a star or non-symmetric letter (like an �F�), cut into a metal sheet. The students are asked to measure the focal length of several lenses, by adjusting source-to-lens (�object�) and lens-to-screen (�image�) distances, to which they apply the thin-lens formula. Students are asked to judge visually when the image is �in focus�. In performing this experiment it is assumed that the index of refraction (n) is independent of wavelength, which is not strictly true. The goal of this work is to show that the �chromatic aberration� can in fact be measured as part of such as exercise, primarily using the equipment that would normally be used for this exercise.

  

Experiment

The equipment used is a 2-meter optical rail, to which are mounted an incandescent light source, a lens holder, and a white screen (the image plane). The �object� is a star cut into a metal sheet, which fits into a slot in front of the ground glass screen. The points of the star do not all have the same shape, which allows the student to see if the final image is erect or inverted. Standard glass lenses are used, though the best results on chromatic aberration are obtained for relatively large focal length lenses (30 cm or greater). The new wrinkle is that color filter sheets are inserted between the ground glass and the object.

The filters used were obtained from Arbor Scientific1, set 33-0190. The three filters of this set used were the red, blue, and green. None of these pass only a single color (wavelength), which is good, since in that case the intensity of the image would be too weak to be observed. The red is a �high pass� filter, allowing wavelengths above about 636 nm to pass. The green and blue are �band-pass� filters, the green being centered at about 521 nm, and the blue being centered at about 428 nm, as per the transmittance spectra that are included with the filter set. (The yellow, cyan, and magenta filters of the set each pass a broader range of wavelengths.) Measurements of the focal length were made using each of these filters, as well with white light (no filter), using a nominal 30 cm focal length lens, and at several image-to-object distances.

The measurements were made by adjusting the position of the lens to obtain a sharply focused image. To avoid a bias in the measurements, the image was �defocused� when each new color filter was inserted. However, on inserting a different color, one could qualitatively observe that the previously focused image was no longer sharp.

While the calculated change in the focal length is relatively small (on the order of 0.5 cm), the distance that the lens is moved to achieve focus can be several centimeters. This precision should be well within the capabilities of the careful student. Lenses with shorter focal lengths were also tried, but in these cases the change in position of the lens, as the color is changed, is within the uncertainty of the measurement (0.1 � 0.2 cm); also, the �range� of focus of even white light is so narrow that convincing results can not be obtained with standard introductTable I: Measured values of focal length and n(l ) for various color filters.