Huygens' principle and phase shift

[paweld]

I wonder why the amplitude of Huygens' wavelet is equal to the amplitude of incident wave multimpled by $$i / \lambda$$. I found this formula in 'Modern Optics' by Guenther p. 335 unfortunately without proof. Has anyone seen the derivation of this fact.

Could you recommend me some good books in optics about wave nature of light.

 

[|squeezed>]

Without knowing the formula that you 're referring to, i can tell that terms like these usually appear from the expansion of the point source (exponent of ik|r-r'|, sometimes referred as Huygens elementary wave) over large distances.

The absolute, classic reference for wave phenomena in optics is Born & Wolf. You can find almost everything there. The figures are very nice and clear.

 

[charng]

Huygens' principle is a fundamental concept in the field of optics that explains how waves propagate through a medium. It states that every point on a wavefront can be considered as a source of secondary spherical waves, which combine to form the overall wavefront at a later time. This principle has been used to explain various phenomena in optics, such as diffraction and refraction.

The phase shift mentioned in your question is related to the wavelength of the incident wave. The formula you have mentioned, where the amplitude of the Huygens' wavelet is equal to the amplitude of the incident wave multiplied by i/λ, is derived from the principle of conservation of energy. This principle states that the total energy of a system remains constant, and in the case of waves, this energy is proportional to the square of the amplitude. Therefore, to conserve the total energy, the amplitude of the secondary wavelet must be adjusted according to the wavelength of the incident wave.

As for recommendations for books on the wave nature of light, I would suggest "Optics" by Eugene Hecht and "Fundamentals of Optics" by Francis A. Jenkins and Harvey E. White. Both of these books provide a comprehensive introduction to the wave nature of light and its applications in optics. Additionally, "Introduction to Optics" by Frank L. Pedrotti and "Principles of Optics" by Max Born and Emil Wolf are also excellent resources for understanding the wave properties of light.