I am currently attempting a physics question on optics.
A Fresnel Zone Plate has overall radius a and contains N half-period zones. The odd-numbered zones are open but the even -numbered zones are covered by glass so as to invert the phase of light passing through them. The zone plate is illuminated with monochromatic, collimated light of wavelength lambda and intensity I0
There are a number of prior steps where the focal length is found to be
the intensity of the focal spot was found to be
and that the radius of the focal spot was approximately equal to the width of the outermost half-period zone at
However, in the final part the question now asks:
Show that along the optic axis the focal spot has a length of 4f/N . Hint the intensity on axis will be zero if the phase change across the first open zone is
However, after several attempts I haven't got anywhere and can't quite picture what is going on. I couldn't find any help online so I was wondering could anyone explain how the length of the focal point occurs and point me in the right direction to solve the problem .
I believe I solved my problem. I found that the two minimums around the focal spot where at f(1+2/N) and f(1-2/N) thus giving my a length of 4f/N.