ps04_solns

# ps04_solns - Physics 1112 Spring 2008 PS#4 Solutions Page 1...

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Unformatted text preview: Physics 1112 Spring 2008 PS #4 Solutions Page 1 of 6 Physics 1112 Problem Set #4 Solutions Problem 1: A simple camera telephoto lens consists of two lenses. The objective lens has a focal length f 1 = + 41 . 1 cm. Precisely 34 . 9 cm behind this lens is a concave lens with a focal length f 2 =- 14 . 2 cm. The object to be photographed is 3 . 84 m in front of the objective lens. (a) How far behind the concave lens should the film be placed? (b) What is the lateral magnification of this lens combination? (a) For this two-lens system, we can treat the effects of each lens individually. So, let’s first determine the image distance produced by the first, objective lens: 1 d o 1 + 1 d i 1 = 1 f 1 = ⇒ 1 d i 1 = 1 f 1- 1 d o 1 . Putting in the numbers we’re given, 1 d i 1 = 1 41 . 1 cm- 1 384 cm = 0 . 0217267 cm − 1 = ⇒ d i 1 = 46 . 026 cm . This real image distance is measured from the first lens. Notice that d i 1 is actually larger than the separation between the lenses, so it is beyond the second, concave lens. In other words, we have a virtual object for the second lens! d o 2 = (34 . 9 cm)- d i 1 =- 11 . 126 cm . Next, let’s apply the thin-lens equation for the concave lens, 1 d o 2 + 1 d i 2 = 1 f 2 = ⇒ 1 d i 2 = 1 f 2- 1 d o 2 , which with our numbers works out to 1 d i 2 = 1- 14 . 2 cm- 1- 11 . 126 cm = 0 . 019455 cm − 1 = ⇒ d i 2 = 51 . 4 cm . (b) The magnification of multiple lenses is just the product of the individual magnifications: m 1 =- d i 1 d o 1 =- 46 . 026 384 =- . 11986 m 2 =- d i 2 d o 2 =- 51 . 4- 11 . 126 = 4 . 6198 m tot = m 1 m 2 =- . 554 . The ray diagram will look qualitatively the same as the diagram for Problem 4, below. Physics 1112 Spring 2008 PS #4 Solutions Page 2 of 6 Problem 2: The barrel of a compound microscope is 13 . 4 cm in length. The specimen will be mounted 1 . 19 cm from the objective, and the eyepiece has a 5 . 09 cm focal length. Determine the focal length of the objective lens....
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ps04_solns - Physics 1112 Spring 2008 PS#4 Solutions Page 1...

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