Arago spot

Photo of the Arago spot in a shadow of a 5.8 mm circular obstacle.
Arago spot experiment. A point source illuminates a circular object, casting a shadow on a screen. At the shadow's center a bright spot appears due to diffraction, contradicting the prediction of geometric optics.
Arago spot forming in the shadow.
Numerical simulation of the intensity of monochromatic light of wavelength λ = 0.5 μm behind a circular obstacle of radius R = 5 μm = 10λ.
Formation of the Arago spot (select "WebM source" for good quality).

In optics, the Arago spot, Poisson spot,[1][2] or Fresnel spot[3] is a bright point that appears at the center of a circular object's shadow due to Fresnel diffraction.[4][5][6][7] This spot played an important role in the discovery of the wave nature of light and is a common way to demonstrate that light behaves as a wave.

The basic experimental setup requires a point source, such as an illuminated pinhole or a diverging laser beam. The dimensions of the setup must comply with the requirements for Fresnel diffraction. Namely, the Fresnel number must satisfy where

  • d is the diameter of the circular object,
  • ℓ is the distance between the object and the screen, and
  • λ is the wavelength of the source.

Finally, the edge of the circular object must be sufficiently smooth.

These conditions together explain why the bright spot is not encountered in everyday life. However, with the laser sources available today, it is undemanding to perform an Arago-spot experiment.[8]

In astronomy, the Arago spot can also be observed in the strongly defocussed image of a star in a Newtonian telescope. There, the star provides an almost ideal point source at infinity, and the secondary mirror of the telescope constitutes the circular obstacle.

When light shines on the circular obstacle, Huygens' principle says that every point in the plane of the obstacle acts as a new point source of light. The light coming from points on the circumference of the obstacle and going to the center of the shadow travels exactly the same distance, so all the light passing close by the object arrives at the screen in phase and constructively interferes. This results in a bright spot at the shadow's center, where geometrical optics and particle theories of light predict that there should be no light at all.

  1. ^ Law, Jonathan; Rennie, Richard (2015), "Poisson's Spot", A Dictionary of Physics, Oxford University Press, p. 444, ISBN 978-0198714743, SBN-10: 0198714742
  2. ^ Hecht, Eugene; Zajac, Alfred (1974), "10.3, "Diffraction,"", Optics (1st ed.), Addison Wesley, p. 374, ISBN 0-201-02835-2
  3. ^ "Although this phenomenon is often called Poisson's spot, Poisson probably was not happy to have seen it because it supported the wave model of light. The spot is sometimes called Fresnel's spot because it is a direct consequence of his work, and Arago's spot because Arago devised the experiment that confirmed its existence." Katz, Debora M., Physics for Scientists and Engineers: Foundations and Connections, Advance Edition, Volume 2, Cengage Learning, 2015. ISBN 1305537203
  4. ^ Cite error: The named reference pedrotti2007 was invoked but never defined (see the help page).
  5. ^ Cite error: The named reference walker2008 was invoked but never defined (see the help page).
  6. ^ Cite error: The named reference ohanian1989 was invoked but never defined (see the help page).
  7. ^ Cite error: The named reference hecht2002 was invoked but never defined (see the help page).
  8. ^ "Poisson's Spot".