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A New Look at Fundamentals of the Photometric Light Transport and Scattering Theory
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 5
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Fig. 2.
Radiant flux
F
(
x
) and a
formation of the flux decrement
inside
the sample with discrete absorbers
One can see, that defining
ln 1 ,
K
a
there is no way to distinguish
between continuous and discrete absorbers media using both the photometric
approach and measurements of
F
(
x
). Despite the stepwise nature of the function
Eq. (4), whose derivative, formally, does not exist at points of location of the
absorbers, i.e., at points of discontinuity of the first kind, a
smooth approximating
curve
for
F
(
x
) can be found with the use of the formal phenomenological approach
Eq. (2). Thus, there is no sense to consider models of discrete absorbers inside the
material medium.
2. Our note 2 concerns the correspondence between photometry and
electromagnetism. In spite of the lack of any needs in phenomenological photometry
to understand the wave nature of light and the Maxwell's electrodynamics,
nevertheless, it is important today to keep in mind the relationship between these two
approaches. Mainly, it concerns the right understanding of the absorption and
scattering properties of different turbid media in which light propagates. Many
articles were published on this issue, but we need to subtract only the simplest
statements what we are going to use for our next ''first principles'' approach. It
consists of the following.
If consider a plane-parallel wave propagating along axis
X
:
0
(
)
0
( , )
,
j kx t
E x t E e
(6)
where
E
0
is the amplitude of the electric field [V/m];
1,
j
2 /
k
is the wave
number [m
−1
];
is the wavelength [m];
0
is the angular (circular) frequency;
t
is
time, then the radiant flux
F
0
incident on the surface
A
at a point
x
is determined by
the equation [1]
2
0
( , ) ,
2
e
A F
E x t
Z
(7)
where
A
is a surface [m
2
];
Z
e
is the wave impedance of the medium [Ohm];
( , )
E x t
is
the time-average field amplitude. It is well-known, that in a material medium the
wave number
k
can be expressed through the complex refractive index
n*
of the me-
dium as follows:
0
0
0
2
*
(
)
(
),
k
n
n j
n j
c
c
(8)
where
c
is the speed of light in vacuum;
n
and
are the real and imaginary parts of
n*
respectively;
0
is the wavelength in a free space. Imaginary part
is proportional to