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

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Light sources at infinity produce plane wavefronts due to the infinite radius of the spherical wavefronts, resulting in zero curvature. In contrast, light sources at finite distances create circular wavefronts because the curvature is still present. Linear light sources, like slits, generate cylindrical waves due to diffraction effects. The relationship between different wavefront shapes can be explained through the superposition of harmonic functions, allowing for conversions between plane and cylindrical harmonics. Understanding these principles is essential for comprehending wavefront behavior in various mediums.
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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.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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