mat-sln-asn-hwk23-spr02 - Solution for Homework 23 Optical...

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Unformatted text preview: 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 first day of class. Suppose a human can confortably live in a spaceship accelerating at 1 g = 9 . 81 m s 2 , ignoring relativistic effects, 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 = 10 7 s . Select One of the Following: (a) 15 . 7yr (b) . 19yr (c-Answer) . 97yr (d) 15 , 000yr (e) Toby. Solution From 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 final image forms from the diverging lens. Select One of the Following: (a) +8 . 1cm (b-Answer)- 9 . 8cm (c) +1 . 5cm (d)- 15cm (e) Toby. Solution (a) The ray diagram is drawn below. 1 Converging Lens 5cm 15cm 25cm-5cm-15cm-25cm object image Ray Diagram Must be Drawn to Scale F F P CC FF f 1 s 1 s 1 (b) Use the Thin Lens Equation for the first lens: 1 f 1 = 1 s 1 + 1 s 1 , where f 1 = 12cm is the focal length of the first lens, s 1 = 22cm is the object distance, and s 1 is the image distance of the first 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 first lens, s 2 = d- s 1 = 55cm- 26 . 4cm = 28 . 6cm . Use the Thin Lens Equation to compute the final 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) Problem: Unpolarized sunlight with intensity 1000 W m 2 is incident on two polarizers, whose transmission axes make an angle of 30 . Calculate the intensity of the transmitted light from the second polarizer. Select One of the Following: 2 (a) 750W / m 2 (b) 430W / m 2 (c-Answer) 375W / m 2 (d) (e) Toby Solution The first polarizer decreases the intensity of the light by 2 , I 1 = I / 2 . The second polarizer further reduces the intensity according to Maluss law, I 2 = I 1 cos 2 30 = ( I / 2) cos 2 30...
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This note was uploaded on 03/29/2010 for the course PHYS 2469 taught by Professor Stewat during the Spring '10 term at University of Arkansas Community College at Batesville.

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mat-sln-asn-hwk23-spr02 - Solution for Homework 23 Optical...

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