Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/427

 

The velocity of propagation is

$V={\frac {n}{q}}$,

(5)

and the coefficient of absorption is

$p=2\pi \mu CV$.

(6)

Let $R$ be the resistance, in electromagnetic measure, of a plate whose length is $l$, breadth $b$, and thickness $z$,

$R={\frac {l}{bzC}}$.

(7)

The proportion of the incident light which will be transmitted by this plate will be

$e^{-2pz}=e^{-4\pi \mu {\frac {l}{b}}{\frac {V}{R}}}$.

(8)

799.] Most transparent solid bodies are good insulators, and all good conductors are very opaque. There are, however, many exceptions to the law that the opacity of a body is the greater, the greater its conductivity.

Electrolytes allow an electric current to pass, and yet many of them are transparent. We may suppose, however, that in the case of the rapidly alternating forces which come into play during the propagation of light, the electromotive force acts for so short a time in one direction that it is unable to effect a complete separation between the combined molecules. When, during the other half of the vibration, the electromotive force acts in the opposite direction it simply reverses what it did during the first half. There is thus no true conduction through the electrolyte, no loss of electric energy, and consequently no absorption of light.

800.] Gold, silver, and platinum are good conductors, and yet, when formed into very thin plates, they allow light to pass through them. From experiments which I have made on a piece of gold leaf, the resistance of which was determined by Mr. Hockin, it appears that its transparency is very much greater than is consistent with our theory, unless we suppose that there is less loss of energy when the electromotive forces are reversed for every semi-vibration of light than when they act for sensible times, as in our ordinary experiments.

801.] Let us next consider the case of a medium in which the conductivity is large in proportion to the inductive capacity.

In this case we may leave out the term involving $K$ in the equations of Art. 783. and they then become