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:

v- the speed of light in medium 1,_{1}

v- the speed of light in medium 2,_{2}

θ- angle of light's deflection in medium 1,_{1}

θ- angle of light's deflection in medium 2,_{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 E^{2} space is given with the following equation:

(10)

⇒

(11)

In anisotropy E^{3} 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´,

Press the following button to download the article in the PDF format: