Diffraction of a circular aperture

AI Thread Summary
The discussion centers on calculating the intensity of light at a point on the central axis after passing through a circular aperture with a diameter of 3.6 mm, using a collimated laser beam of wavelength 600 nm and intensity 10 W/m². Participants express confusion about whether to apply Fraunhofer or Fresnel diffraction principles, noting that a circular aperture typically produces an Airy disk pattern. There is a specific concern regarding the Bessel function's behavior, particularly that while J1(x) is zero at x=0, the limit of J1(x)/x is finite, which suggests the intensity should not be zero at the center. The need for clarification on the application of diffraction equations and the interpretation of the resulting intensity is emphasized. Overall, the thread seeks guidance on resolving these diffraction-related calculations.
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Homework Statement


A collimated laser beam ( λ=600 nm) having an intensity I=10 W/m2 is incident
perpendicularly on an opaque screen containing a circular hole with diameter
D=3.6 mm. Calculate the intensity at a point on the central axis that is distanced
180 cm from the screen.

Homework Equations



I=4I0\left(\frac{J(kaq/R)}{(ka/R)})^2

The Attempt at a Solution



firstly I am confused if i should treat this as Fraunhofer or Fresnel diffraction. I know that for a circular aperture it will form an airy disk, but that will leave the bessel function = 0, which means the resulting intensity is zero. (that would make sense if the center is dark, ut it should be bright.

I really think I am missing something simple here. please help.
 
Physics news on Phys.org
It is true that the J1(x) Bessel function is zero at x=0, but J1(x)/x has a finite limit.

ehild
 

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