MIT2_71S09_ufinal_sol

# MIT2_71S09_ufinal_sol - 2.71 Optics Final Exam Solutions...

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Optics Final Exam Solutions Spring ‘09 1. Consider the following system. (a) If we position an on-axis point source at the center of the object plane (front focal plane of L1), a collimated ray bundle will emerge to the right of L1 and its diameter is set by S1; therefore, S1 is the aperture stop (A.S.). Similarly, S2 limits the lateral extent of an imaged object (consider an oﬀ-axis point source) and thus, it’s our ±eld stop (F.S.). (b) The entrance pupil is the image of the A.S. by the preceding optical components. To ±nd its location we use the imaging condition, 1 1 1 S o f 1 2 f 1 2 / 3 + = S i = = S o S i f 1 S o f 1 f 1 ( 2 3 1) 2 f 1 S o = S i = 2 f 1 (virtual) 3 So the entrance pupil is located at 2 f 1 to the right of L1. To ±nd its radius, we compute the lateral magni±cation, S i M L = S o = 3 r EnP = 3 a 1 For the exit pupil (Ex.P.), f 1 ( f 3 1 + f 2 ) f 2 f 2 2 S o = + f 2 , S i = = f 2 + 3 (to the right of L2) 3 f 1 f 1 + f 2 3 f 2 + f 2 ) 3 f f 1 2 ( f 3 1 f 2 f 2 M L = ( f 1 + f 2 ) = 3 f 1 (inverted) r ExP = 3 f 1 a 1 3 The exit window is the same as S2. The entrance window is the image of S2 through

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MIT2_71S09_ufinal_sol - 2.71 Optics Final Exam Solutions...

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