How Do Infinite and Finite Light Sources Produce Different Wavefront Shapes?

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Kehsibashok
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1.how and why does a light source in an isotropic medium at INFINITY produces PLANE Wavefronts instead of CIRCULAR Wavefronts as in case , when a light source is in the same isotropic medium but at FINITE distance?

2.how and why does a linear source of light such as a slit illuminated , produces CYLINDRICAL waves?
 
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1. Spherical wavefronts change into plane wavefronts at infinity, because the radius of the sphere grows with the distance. A sphere with infinite radius has zero curvature: it is a plane.

2. This is caused by diffraction.
 
We can describe any (scalar) field as a linear sum of harmonic functions, be they planar (cartesian), cylindrical or spherical.

For example, a plane wave can be described as a sum of cylindrical harmonics. A cylindrical harmonic can conversely be described as a sum of plane waves.

Claude.