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Unformatted text preview: Solution for Homework 22 Optical Elements Solution to Homework Problem 22.1(Focal Length of Diverging Lens) Problem: Im playing with the optics kit we bought my eldest daughter when she was four. The set contains a diverging lens made out of some kind of glass with index of refraction of about 1 . 6 . The focal length of the lens is | f | = 5cm . If one surface of the lens is planar and the other is curved. What is the radius of curvature of the curved surface? Assume light reaches the curved surface first and report the radius of curvature with the correct sign. Select One of the Following: (a) 3cm (b-Answer)- 3cm (c) 6cm (d)- 6cm (e) Toby. Solution If light reaches the curved surface first we have n = 1 . 6 , r 2 = . The focal length is negative for a diverging lens, f =- 5cm . The lens makers equation gives us 1 f = ( n- 1) parenleftbigg 1 r 1- 1 r 2 parenrightbigg = ( n- 1) 1 r 1 so r 1 = f ( n- 1) =- 5cm(1 . 6- 1) =- 3cm Total Points for Problem: 3 Points Solution to Homework Problem 22.2(Describe Image from Magnification) Problem: An image has magnification . 5 . Which of the following describes the image? Select One of the Following: (a) enlarged, upright. (b) enlarged, inverted. (c) reduced, inverted. (d-Answer) reduced, upright. Solution Since | m | &lt; 1 , the image is reduced. Since m &gt; , the image is upright. Total Points for Problem: 2 Points Solution to Homework Problem 22.3(Focal Length of Isolated Sphere) Problem: In the capacitance lab, we calculated the capacitance of an isolated conducting sphere. You measured the radius of the sphere as 12 . 5cm . If you look at the sphere you see an image of yourself in it. Calculate the focus length of the sphere with correct sign....
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- Winter '08