- #1

PhilDSP

- 643

- 15

On page 122 of Born and Wolf's "Principles of Optics" the following equation for the trajectory of a ray of light is glibly derived in association with the eikonal equation.

[tex]\frac{d}{d \bf s} (n \frac{d \bf r}{d \bf s}) = \nabla n[/tex]

where n is the index of refraction and r is the displacement vector

This equation is extremely interesting because much earlier J. J. Thomson developed it into an equation of motion for the electron. But details in its derivation are sadly missing in both places.

What are the limitations? Does the equation degenerate as the wavelength approaches zero? Does anyone have references to a more detailed derivation?

[tex]\frac{d}{d \bf s} (n \frac{d \bf r}{d \bf s}) = \nabla n[/tex]

where n is the index of refraction and r is the displacement vector

This equation is extremely interesting because much earlier J. J. Thomson developed it into an equation of motion for the electron. But details in its derivation are sadly missing in both places.

What are the limitations? Does the equation degenerate as the wavelength approaches zero? Does anyone have references to a more detailed derivation?

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