Arago Spot

In optics, an Arago spot, Fresnel bright spot, or Poisson spot is a bright point that appears at the center of a circular object's shadow due to Fresnel diffraction. This spot played an important role in the discovery of the wave nature of light (see history section below) and is a common way to demonstrate that light behaves as a wave for example in undergraduate physics laboratory exercises. The basic experimental setup is shown in the figure on the right. The wave source must be at least smaller in diameter than the circular object casting the shadow and 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

λ 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 abundance of laser sources available today it is easy to perform an Arago spot experiment (see for example here). In astronomy, the Arago spot can be also easily 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.

The presence of the Arago spot can be easily understood. When light shines on a 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.