Diffraction of a circular aperture

In summary, a collimated laser beam with a wavelength of 600 nm and an intensity of 10 W/m2 is incident on an opaque screen containing a circular hole with a diameter of 3.6 mm. We need to calculate the intensity at a point on the central axis that is 180 cm away from the screen. The resulting intensity will depend on whether we treat this as Fraunhofer or Fresnel diffraction. For a circular aperture, it will form an airy disk, but the Bessel function will be zero at the center, resulting in a zero intensity. However, the J1(x)/x function has a finite limit, which may lead to a non-zero intensity. Further clarification is needed to determine the
  • #1
groosagi
2
0

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[tex]\left([/tex][tex]\frac{J(kaq/R)}{(ka/R)}[/tex])^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.
 
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  • #2
It is true that the J1(x) Bessel function is zero at x=0, but J1(x)/x has a finite limit.

ehild
 

What is diffraction of a circular aperture?

Diffraction of a circular aperture is a phenomenon that occurs when a wave, such as light or sound, passes through a circular opening. The wave bends and spreads out as it passes through the aperture, creating a diffraction pattern.

What factors affect the diffraction pattern of a circular aperture?

The size of the aperture and the wavelength of the wave are the two main factors that affect the diffraction pattern of a circular aperture. The smaller the aperture or the longer the wavelength, the more pronounced the diffraction pattern will be.

What is the difference between Fresnel and Fraunhofer diffraction?

Fresnel and Fraunhofer diffraction are two types of diffraction that occur when a wave passes through a circular aperture. Fresnel diffraction occurs when the aperture and the observation point are at different distances from the wave source, while Fraunhofer diffraction occurs when the aperture and the observation point are at a large distance from the wave source.

How can diffraction of a circular aperture be used in real-life applications?

Diffraction of a circular aperture has many practical applications, such as in astronomy, where it is used to study the diffraction patterns of stars and galaxies. It is also used in photography to create artistic effects, and in microscopy to improve the resolution of images.

How can the diffraction pattern of a circular aperture be calculated?

The diffraction pattern of a circular aperture can be calculated using the Huygens-Fresnel principle, which states that every point on a wavefront can act as a source of secondary waves. By considering the contributions of all these secondary waves, the overall diffraction pattern can be determined.

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