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MIT2_71S09_practice1_sol

# MIT2_71S09_practice1_sol - 2.71/2.710 Optics Practice Exam...

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2.71/2.710 Optics Practice Exam 1 - Solutions Spring ‘09 1. Consider the two-lens system shown below. Lens L1 has focal length f , and lens L2 has focal length f/ 2. (a) Set the separation distance d such that the Effective Focal Length (EFL) of the combination equals f . Solution: Using the matrix method, � � � � � � 1 f 2 1 0 1 f 1 = 1 2 f d f 3 2 f d 0 1 d 1 0 1 d 1 f d 3 2 d The power of this system is: P = f f 3 2 d 1 In order to make the EFL = f , we have: = d = f f f f 1

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(b) Locate the principal planes. Solution: The BFP and 2nd principle plane are very easy to find. Because d = f , the parallel rays pass through L1 and focus at the center of L2. Thus L2 has no effect on these rays. The BFP is at the center of L2 and the 2nd PP is at L1. The FFP and 1st PP can be obtained by thinking about parallel rays coming from right to left. After passing through L2, they focus at the distance of f/ 2 to L2. Thus, to lens L1, the object distance is: f f f S o = d = f = 2 2 2 1 1 1 S o + S i = f S i = f The FFP is also at the center of L2. The 1st PP is located at a distance f to the right of lens L2.
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MIT2_71S09_practice1_sol - 2.71/2.710 Optics Practice Exam...

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