_022 - Solution for Homework 23 Optical Systems Solution to Homework Problem 23.1(How long to accelerate to light speed Problem A problem you

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Solution for Homework 23 Optical Systems Solution to Homework Problem 23.1(How long to accelerate to light speed?) Problem: A problem you should have easily been able to do in UPI, but I get asked it all the time when I ask for a good question on electricity and magnetism the Frst day of class. Suppose a human can confortably live in a spaceship accelerating at 1 g = 9 . 81 m s 2 , ignoring relativistic e±ects, how long does it take the spaceship to reach the speed of light? Report your answer in years. You may use the approximate conversion 1yr = π × 10 7 s . Select One of the ²ollowing: (a) 15 . 7yr (b) 0 . 19yr (c-Answer) 0 . 97yr (d) 15 , 000yr (e) Toby. Solution ²rom UPI, v = at = gt , so t = c g = 3 × 10 8 m s 9 . 81 m s 2 = 3 . 05 × 10 7 s = 0 . 97yr Total Points for Problem: 3 Points Solution to Homework Problem 23.2(Two Lens Problem) Problem: A converging lens of focal length 12cm and a diverging lens of focal length - 15cm are separated by 55cm . An object is placed 22cm to the left of the converging lens. Compute the distance (with correct sign) the Fnal image forms from the diverging lens. Select One of the ²ollowing: (a) +8 . 1cm (b-Answer) - 9 . 8cm (c) +1 . 5cm (d) - 15cm (e) Toby. Solution (a) The ray diagram is drawn below. 1

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Converging Lens 5cm 15cm 25cm -5cm -15cm -25cm object image Ray Diagram Must be Drawn to Scale F’ F 0 P CC FF f 1 s 1 s 1 (b) Use the Thin Lens Equation for the Frst lens: 1 f 1 = 1 s 1 + 1 s 1 , where f 1 = 12cm is the focal length of the Frst lens, s 1 = 22cm is the object distance, and s 1 is the image distance of the Frst lens. Solve for s 1 s 1 = 1 1 f 1 - 1 s 1 . s 1 = 1 1 12cm - 1 22cm = 26 . 4cm (c) The object distance for the second lens is the separation of the lenses, d , minus the image distance of the Frst lens, s 2 = d - s 1 = 55cm - 26 . 4cm = 28 . 6cm . Use the Thin Lens Equation to compute the Fnal image distance, s 2 . s 2 = 1 1 f 2 - 1 s 2 , where f 2 = - 15cm is the focal length of the second lens. Solve for s 2 : s 2 = 1 1 f 2 - 1 s 2 = 1 1 15cm - 1 28 . 6cm = - 9 . 8cm Total Points for Problem: 3 Points Solution to Homework Problem 23.3(Crossed Polarizers)
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This note was uploaded on 05/04/2008 for the course PHYS 2074 taught by Professor Stewart during the Winter '08 term at Arkansas.

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_022 - Solution for Homework 23 Optical Systems Solution to Homework Problem 23.1(How long to accelerate to light speed Problem A problem you

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