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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

Inquiry into Physics
Inquiry into Physics
8th Edition
ISBN:9781337515863
Author:Ostdiek
Publisher:Ostdiek
Chapter9: Optics
Section: Chapter Questions
Problem 14P: . (a) In a camera equipped with a 50-mm focal-length lens, the maximum distance that the lens can be...
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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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