The fraction of light incident on a circular aperture (normal incidence) that is transmitted is given by 2ka 2 1 T = [th 42(x) (3/3 - 2/2 a) dx, 2ka where a is the radius of the aperture, and k is the wave number, 2л/λ. Show that (a) T=1- ka n=0 J2n+1(2ka), (b) T=1- 1 2ka 2ka Jo(x) dx.
The fraction of light incident on a circular aperture (normal incidence) that is transmitted is given by 2ka 2 1 T = [th 42(x) (3/3 - 2/2 a) dx, 2ka where a is the radius of the aperture, and k is the wave number, 2л/λ. Show that (a) T=1- ka n=0 J2n+1(2ka), (b) T=1- 1 2ka 2ka Jo(x) dx.
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Transcribed Image Text:12.1.15 The fraction of light incident on a circular aperture (normal incidence)
that is transmitted is given by
1
ka
2ka
= [2 12₂(x) ( ² 2 - 2 1 4 ) dx,
2ka
T =
where a is the radius of the aperture, and k is the wave number, 2л /λ.
Show that
(a) T=1-
ΣJ2n+1(2ka), (b) T=1-
n=0
1 2ka
i So
2ka
Jo (x) dx.
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