Diffraction of a circular aperture

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SUMMARY

The discussion centers on calculating the intensity of light at a point on the central axis of a circular aperture due to diffraction. A collimated laser beam with a wavelength of 600 nm and intensity of 10 W/m² is incident on a circular hole with a diameter of 3.6 mm. The relevant equation for intensity is I=4I0(J(kaq/R)/(ka/R))². The confusion arises between Fraunhofer and Fresnel diffraction, with emphasis on the behavior of the Bessel function J1(x), which is zero at x=0 but has a finite limit when divided by x.

PREREQUISITES
  • Understanding of diffraction principles, specifically Fraunhofer and Fresnel diffraction.
  • Familiarity with Bessel functions and their properties.
  • Knowledge of laser beam characteristics, including wavelength and intensity.
  • Ability to apply mathematical equations related to wave optics.
NEXT STEPS
  • Study the derivation and applications of the Bessel function in optics.
  • Learn about the differences between Fraunhofer and Fresnel diffraction.
  • Explore the concept of Airy disks and their significance in circular apertures.
  • Investigate numerical methods for calculating diffraction patterns in complex scenarios.
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Students and professionals in optics, physicists working with wave phenomena, and anyone involved in laser applications and diffraction analysis.

groosagi
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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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