Abstract

        The article shows that the essential equation of light trajectory is very simple and that it is connected with the third derivative of the coordinate oppositely than the classic mechanics where the second derivative is the last significant one.
         The goal of the article is following formula:

(9)

Above formula yields connection between velocity and declination.

EQUATION OF LIGHT TRAJECTORY

Let start from the well-known equation of light refraction:

(1)

Whereas:

v1 - the speed of light in medium 1,
v2 - the speed of light in medium 2,
θ1 - angle of light's deflection in medium 1,
θ2 - angle of light's deflection in medium 2,

        We can suppose that the mediums are nearly equals and that the light speeds are also nearly equals, than we have:

(2)

(3)

It can be derived directly:

(4)

(5)

(6)

(7)

After the both sides of equation are differentiated by θ, hence is obtained:

(8)

Finally:

(9)

Regarding the image:

        This is the final equation of the light trajectory, which gives the basic relation between path of the light beam and its differential declination.
         Evaluated equation for E2 space is given with the following equation:

(10)

(11)

In anisotropy E3 space the equation has the next form:

(12)

 

        This is the final light beam trajectory equation. It shows that in light mechanics great influence has the third time derivation of coordinate related the classic mechanics where the second derivative is the last substantially significant one. It also shows that the light must change the speed near the rigid bodies' edges and in gaps too.
         The equation could be used as test-bench for the new theories of the electromagnetic and their equations that have to satisfy it.

Author:
Dipl. Ing. Andrija S. Radovic
Tel: +381 64 1404075
andrijar@andrijar.com


        Author of this article and all its formulas is Andrija S. Radovic, Journal Of Theoretics, all rights reserved. The parts or all the article can not be published without Journal's prior agreement and without Journal's and author's name below text.

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