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Unformatted text preview: Solution for Homework 22 Optical Elements Solution to Homework Problem 22.1(Image Distance From Convex Mirror) Problem: A convex mirror has a radius of curvature of magnitude | r | = 50 . cm . An object is 20 . cm from the mirror. Compute the image distance. Select One of the Following: (a)- 14cm (b)- 33cm (c-Answer)- 11cm (d)- 100cm (e) Toby. Solution A convex mirror has a negative focal length and the focal length is half the radius of curvature, f =-| r | / 2 =- 25cm . The image is located using the thin lens equation, 1 f = 1 s + 1 s where the object distance is s and the image distance is s . 1 s = 1 f- 1 s 1 s = 1- 25cm- 1 20cm s =- 100 9 cm =- 11cm Total Points for Problem: 3 Points Solution to Homework Problem 22.2(Old Masters Trick) Problem: In the Physics of Art Talk, some of the Old Masters used a concave mirror to project the image of a subject on a screen so they could trace the subject and get the perspective right. In the example the speaker presented, the object distance appeared to be about 10ft and the image distance about 3ft . Compute the radius of curvature of the mirror used. Report the radius with the correct sign. Select One of the Following: (a) 9 . 3ft (b-Answer) 4 . 6ft (c) - 4 . 3ft (d) 2 . 3ft (e) Toby. 1 Solution Apply the thin lens equation to find the focal length, 1 s + 1 s = 1 f = 1 10ft + 1 3ft Solving for f gives f = 2 . 3ft . The mirror makers equation then gives r = 2 f = 4 . 6ft Total Points for Problem: 3 Points Solution to Homework Problem 22.3(Changing Earths Electric Field Problem) Problem: The Earths electrical field changes locally due to thunderstorm activity. Suppose the earths electric field changes from its normal value of 150 N C to zero in an hour following the function, E ( t ) = E e t/ where E = 150 N C and = 1 . 10 3 s . The earths field points radially downward. Compute the displacement current through a circular hoop of radius . 50m at t = 0 lying on the ground....
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