MIT2_71S09_gps5 - interferometer with a lens inserted in...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.710 Optics Spring ’09 Problem Set #5 Posted Monday, March 30, 2009 — Due Wednesday, April 8, 2009 1. Two plane waves of the same wavelength λ are propagating along the directions of wave vectors k 1 , k 2 as shown in the ±gure below. 1.a) Describe the interference pattern that would be observed on the plane xy . 1.b) Describe the interference pattern that would be observed on a plane parallel to xy but one wavelength λ away towards the positive z direction. 1.c) Describe the interference pattern that would be observed on the plane yz . o y x z k k 30 1 2 45 o o 30 Figure A 2. A plane wave and a spherical wave, both of the same wavelength, are co-propagating as shown in ±gure B on the next page. 2.a) Describe the interference pattern that would be observed on a plane per- pendicular to the z axis at a distance of 1000 λ away from the origin of the spherical wave. 2.b) Repeat for the plane located 2000 λ away from the origin of the spherical wave. 2.c) What do you observe? Explain in physical terms.
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2.d) What is the relationship between your result and a Michelson
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Unformatted text preview: interferometer with a lens inserted in one of the two arms? 1 1000 2000 spherical wave k x z Figure B 3. Repeat the calculations of the previous problem for the case when the plane wave is propagating o-axis as shown in Figure C below. Explain the dierences that you observe. o 1 1000 2000 x z spherical wave 30 k Figure C 4. A fan of N plane waves are propagating symmetrically with respect to the z axis, as shown in gure D below. The angular spacing between successive members of the fan is xed and equal to . Describe the interference pattern observed on a plane perpendicular to the z axis. 2 z n= n=N 1 x Figure D 5. Describe the interference pattern between two counter-propagating plane waves. This is also known as a standing wave. Explain why. 3 MIT OpenCourseWare http://ocw.mit.edu 2.71 / 2.710 Optics Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.710 taught by Professor Sebaekoh during the Spring '09 term at MIT.

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MIT2_71S09_gps5 - interferometer with a lens inserted in...

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