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In Bessel's method for measuring the focal length ƒ of a positive lens, a small object and a white screen are set at a fixed separation L, where L > 4f. The lens is moved along a line through the object perpendicular to the screen, and it is found that there are two lens positions where a sharply focused image is produced on the screen, one magnified and one demagnified. The separation between these two lens positions is then measured as distance D. Prove that the lens focal length is given by L² - D² f 4L

In Bessel's method for measuring the focal length ƒ of a positive lens, a small object and a white screen are set at a fixed separation L, where L > 4f. The lens is moved along a line through the object perpendicular to the screen, and it is found that there are two lens positions where a sharply focused image is produced on the screen, one magnified and one demagnified. The separation between these two lens positions is then measured as distance D. Prove that the lens focal length is given by L² - D² f 4L

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter38: Refraction And Images Formed By Refraction
Section: Chapter Questions
Problem 126PQ
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In Bessel's method for measuring the focal length ƒ of a positive lens, a small object and a white screen are set at a fixed separation L, where L > 4f. The lens is moved along a line through the object perpendicular to the screen, and it is found that there are two lens positions where a sharply focused image is produced on the screen, one magnified and one demagnified. The separation between these two lens positions is then measured as distance D. Prove that the lens focal length is given by L² - D² f 4L
Transcribed Image Text:In Bessel's method for measuring the focal length ƒ of a positive lens, a small object and a white screen are set at a fixed separation L, where L > 4f. The lens is moved along a line through the object perpendicular to the screen, and it is found that there are two lens positions where a sharply focused image is produced on the screen, one magnified and one demagnified. The separation between these two lens positions is then measured as distance D. Prove that the lens focal length is given by L² - D² f 4L
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