ps08soln - PHYSICS 218 SOLUTION TO HW 8 Created: November...

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PHYSICS 218 SOLUTION TO HW 8 Created: November 12, 2004 6:15 pm Last updated: November 15, 2004 1. (a) Using Snell’s law, the incident and refracted angle are related by n 3 sin ϑ 3 = n 2 sin ϑ c . At critical angle, ϑ 3 = π 2 , this gives us ϑ c = arcsin( n 3 /n 2 ). With n 2 =1 . 5 and n 3 . 45, we get ϑ c = arcsin(1 . 45 / 1 . 5) = 75 . 16 . (b) Applying Snell’s law again at the n 1 - n 2 boundary, we have n 1 sin ϑ 1 = n 2 sin ϑ 2 . Since ϑ 2 = π/ 2 ϑ c , we Fnd ϑ 1 = arcsin[( n 2 /n 1 ) cos ϑ c ] = arcsin[(1 . 5 / 1 . 00) cos(75 . 16 )] = 22 . 59 . Hence, the maximum incident angle ϑ 1 for which the entering light will be totally reflected at the Fber-cladding boundary is ϑ 1 =22 . 59 . (c) If there were no cladding, similar to calculations in the previous part, we Fnd ϑ 0 c = arcsin(1 . 00 / 1 . 5) = 41 . 81 , and so sin ϑ 0 1 . 118. This means that ϑ 0 1 2. That is, all light entering the end of the Fber will be totally internally reflected at the Fber-air boundary. (d) ±or both Fbers, the velocity of light in the medium with refraction index n 2 is v = c 0 /n 2 = 1 . 999 × 10 8 ms 1 . ±or the clad Fber, the velocity along the axis of the Fber is then given by v z = v cos ϑ 2 = v sin ϑ c . 999 × 10 8 × sin(75 . 16 )=1 . 932 × 10 8 ms 1 . ±or the unclad Fber, the velocity along the axis of the Fber is v 0 z = v sin ϑ 0 c . 999 × 10 8 × sin(41 . 81 . 332 × 10 8 ms 1 . Hence the range of velocities for the clad and unclad Fber are respectively 1 . 932 × 10 8 v z 1 . 999 × 10 8 ms 1 and 1 . 332 × 10 8 v 0 z 1 . 999 × 10 8 ms 1 . Alternately, for the cladded Fber, we hae a range of velocities between 0 . 967 v and v , while for the uncladded Fber we would have a range between 0 . 667 v and v . The velocity dispersion in the unclad Fber is very large, so signals would get “washed out” quickly as they travel down the Fber. This would not be very useful for communication! On the other hand, the much smaller velocity dispersion in the clad Fber would result in a much larger length before the signals would be washed out.
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This note was uploaded on 09/28/2008 for the course PHYS 218 taught by Professor Pollack during the Fall '04 term at Cornell University (Engineering School).

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ps08soln - PHYSICS 218 SOLUTION TO HW 8 Created: November...

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