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dimestorelaser

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An optical systems consists of 4 lenses spaced apart. Each lens has a focal length f. Each lens is located a distance "z" away from each plane as shown. The total length of the system is 8z.

Find the distance z needed to satisfy a FOURIER TRANSFORM condition between planes P1 and P3. This is equivalent to finding the imaging condition between planes P1 and P5, but is an easier problem to do. Note that there should be 2 answers. Discuss what the output represents for each of these systems.

Some direction and help on this problem would be beneficial.

The problem comes with an image. P1 is plane 1 and is located before the first lens ...there is a plane between each lens for a total of 5.

Its supposed to be easy, I am just having trouble with it. Thanks!