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

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SUMMARY

Infinite light sources in an isotropic medium produce plane wavefronts due to the infinite radius of the spherical wavefront, resulting in zero curvature. In contrast, finite light sources generate circular wavefronts because they maintain a finite radius. Additionally, linear light sources, such as slits, produce cylindrical waves due to diffraction effects. This phenomenon can be mathematically described using harmonic functions, where plane waves can be expressed as sums of cylindrical harmonics and vice versa.

PREREQUISITES
  • Understanding of wavefront shapes in optics
  • Familiarity with isotropic media properties
  • Knowledge of diffraction principles
  • Basic grasp of harmonic functions in physics
NEXT STEPS
  • Study the principles of wavefront propagation in isotropic media
  • Explore the mathematical formulation of diffraction and its effects on wavefronts
  • Learn about cylindrical harmonics and their applications in wave theory
  • Investigate the relationship between plane waves and cylindrical waves in optics
USEFUL FOR

Physicists, optical engineers, and students studying wave optics who seek to understand the differences in wavefront shapes produced by various light sources.

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.
 

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