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by
Richard T. Brundage
Department of Physics, Astronomy, and Engineering Science
St. Cloud State University, St. Cloud, MN
This case was presented to non-science students in a course using optics to illustrate methods and applications of science. The textbook for the course is Seeing the Light: Optics in Nature, Photography, Color, Vision, and Holography by David Falk, Dieter Brill and David Stork, New York: 1986, John Wiley & Sons. The case was assigned as a group project about half-way through the one-semester class. The students had done four cases before that were not as open-ended as this one, so they had experience working together on more straightforward problems. The case is supported by readings, homework problems, and a lab exercise.
This case could be used as a homework assignment. However, it goes beyond the normal individual assignment because there is no single right answer, and it draws together several concepts into one problem. When used as a group assignment, the students work on the problem individually before meeting together to share their ideas. Presumably they will have different solutions concerning what settings to recommend and will have to work out these differences in the group discussion.
The case illustrates the competing demands for light and depth of field in photography. Both are controlled in part by the f/# setting of the camera, which is the diameter of the lens aperture divided by the focal length of the lens. The amount of light power per unit area of film in a camera is proportional to the inverse square of the f/# of the camera lens. The dependence on aperture diameter is obvious: a larger aperture collects more light from the source, varying as the area of the aperture or as the diameter squared. The focal length of the lens determines the size of the image on the film that the light will be spread over. The area of the image will be proportional to the square of the focal length for distant sources. The power per unit film area in the image is the light collected from the source divided by the size of the image of the source.
You can compensate for low light power by exposing the film to the light for a longer period of time. This illustrates the general relationship between power and energy: energy is the power accumulated over a period of time. Film requires a certain amount of light energy per unit area to be exposed, which is expressed in terms of the speed of the film. Fast film requires less light energy than slow film. The amount of energy per unit area of film will be proportional to the product of the light power per unit area and the exposure time. For a given speed film, it will take longer to accumulate enough light energy to expose the film when using a large f/# than it will using a small f/# lens.
The range of distances from the camera that will be in focus on the film, or depth of field, also depends on the f/#, with larger f/#’s giving a greater depth of field. The mathematical dependence of depth of field on f/# is more complicated than the light power per unit area, and is not explored in this course. Details can be found in Introduction to Optics, 2nd ed., Frank L. Pedrotti and Leno S. Pedrotti, New Jersey: 1993, Prentice Hall, pp.125-130.
Every photographer must compromise between the exposure time and the depth of field by choosing an f/# and exposure time that properly exposes the film. A doubling of f/# from f/8 to f/16 to increase the depth of field requires increasing the exposure time by a factor of four. This may be acceptable for a stationary object, but results in blurring if the object moves appreciably during the exposure time.
The case was designed to highlight this compromise by making simultaneous demands for both large depth of field and short exposure time. It also illustrates the reciprocal nature of exposure time and f/# by showing that two different pairs of settings can lead to proper exposure of the film. Finally, it points out that there are considerations outside of the basic science of photography that can determine the “best” settings for a given photograph. This allows members of the group to take different stands on the solution to the problem and realize that there is no one correct answer.
Students are assigned Chapter 4 of the text, The Camera and Photography, to read, and several homework problems on the effect of focal length, f/# and exposure time on photographs. They carry out a lab exercise where the variation in image size with focal length is used to measure the focal length of some camera lenses, and where the effect of f/# on brightness and depth of field is observed. They receive the case story and assignment several days before the class meeting when the assignment is completed. They are divided into heterogeneous groups according to class performance early in the term and have completed several group assignments before this one.
Each person in the group is assigned a role:
The roles rotate during the term.
Approximately 30 minutes of one class period are devoted to the students working together in their groups to arrive at a written solution to the problem. The instructor circulates among the groups and answers and poses questions as needed.
I have included in the answer key a brief example of one of the better project solutions that I received. The most common mistake I observed was that students tended to neglect discussion of depth of field and talk only of exposure time versus f/#. Another problem was the lack of a single solution. Groups often hedged their bets by offering several different settings, with varying levels of discussion about how the results would vary for each setting. The case assignment was modified to insure that groups had to come up with one final solution.
The effects illustrated in the photographs accompanying the case can also be demonstrated using a single lens reflex camera that allows the aperture to be set while looking through the view finder (see the handout for the images presented as a page of separate supporting material). Some SLR’s do not set the aperture until the shutter is tripped, others, such as some Olympus cameras, have a button you can push to show what the current aperture setting will look like. The effect on the brightness of the image is obvious, it is a little harder to ignore the change in brightness and see the effect on depth of field.
A historical note: Some students may be interested in the work of the “Group f/64” photographers including Ansel Adams, Imogen Cunningham, Edward Weston, and others. They were “in favor of sharply focused images that exploited to the fullest the characteristics of photographic images, rather than attempting to make photographs look like paintings or other graphic media.” (Examples: The Making of 40 Photographs, Ansel Adams, Boston: 1983, Little Brown & Co., pg 29-30.)
Answers to the questions posed in the case study are provided in a separate answer key to the case. Those answers are password-protected. To access the answers for this case, go to the key. You will be prompted for a username and password. If you have not yet registered with us, you can see whether you are eligible for an account by reviewing our password policy and then apply online or write to answerkey@sciencecases.org.
Acknowledgements: This case was developed as part of a National Science Foundation-sponsored Case Studies in Science Workshop (NSF Award #9752799) held at the State University of New York at Buffalo on June 1-5, 1998.
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