Homework 23 Solutions

Homework 23 Solutions - lim (kl9356) Homework 23 Weathers...

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Unformatted text preview: lim (kl9356) Homework 23 Weathers (22202) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points The left face of a biconvex lens has a radius of curvature of 18 . 8 cm, and the right face has a radius of curvature of 15 . 8 cm. The index of refraction of the glass is 1 . 44. Calculate the focal length of the lens. Correct answer: 19 . 5113 cm. Explanation: Given : R 1 = 18 . 8 cm , R 2 =- 15 . 8 cm , and n = 1 . 44 . Using the lens makers equation, 1 f = ( n- 1) parenleftbigg 1 R 1- 1 R 2 parenrightbigg = ( n- 1)( R 2- R 1 ) R 1 R 2 f = R 1 R 2 ( n- 1)( R 2- R 1 ) = (18 . 8 cm)(- 15 . 8 cm) (1 . 44- 1)(- 15 . 8 cm- 18 . 8 cm) = 19 . 5113 cm . 002 (part 2 of 2) 10.0 points Calculate the focal length if the radii of cur- vature of the two faces are interchanged. Correct answer: 19 . 5113 cm. Explanation: Given : R 1 = 15 . 8 cm and R 2 =- 18 . 8 cm . 1 f = ( n- 1) parenleftbigg 1 R 1- 1 R 2 parenrightbigg = ( n- 1)( R 2- R 1 ) R 1 R 2 f = R 1 R 2 ( n- 1)( R 2- R 1 ) = (15 . 8 cm)(- 18 . 8 cm) (1 . 44- 1)(- 18 . 8 cm- 15 . 8 cm) = 19 . 5113 cm . 003 (part 1 of 2) 10.0 points Two converging lenses, each of focal length 15 cm, are placed 39 . 7 cm apart, and an object is placed 29 . 4 cm in front of the first. How far from the first lens is the final image formed? Correct answer: 16 . 7253 cm. Explanation: Given : f 1 = f 2 = 15 cm , L = 39 . 7 cm , and p 1 = 29 . 4 cm . The thin lens equation gives the image po- sition of the first lens as q 1 = p 1 f 1 p 1- f 1 = (29 . 4 cm) (15 cm) 29 . 4 cm- 15 cm = 30 . 625 cm . The real image formed by the first lens serves as the object for the second lens, so p 2 = L- q 1 = 39 . 7 cm- 30 . 625 cm = 9 . 075 cm. Then, the thin lens equation gives q 2 = p 2 f 2 p 2- f 2 = (9 . 075 cm) (15 cm) 9 . 075 cm- 15 cm =- 22 . 9747 cm Thus, the final image is located 16 . 7253 cm front of the second lens, and 16 . 7253 cm be- hind the first lens. 004 (part 2 of 2) 10.0 points What is the magnification of the system?...
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Homework 23 Solutions - lim (kl9356) Homework 23 Weathers...

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