Dispersion of light
§ 1 Method the observation of dispersion.
Prismatic and diffraction spectra. Method Rozhdestvenskiy.
The phenomenon of dispersion is that the refractive index depends on the wavelength.
in Fig. is prismatic. Violet waves are refracted more red, as
wavelength red waves more than the purple, and the frequency,
respectively, lower the refractive index of red waves will be smaller
than the purple.
Prism is often used in spectroscopy (spectroscopy (spectrometer, spectrograph) (from the range in the ancient Greek. Σκοπ?ω
- see) - an optical instrument for visual observation of the radiation
spectrum. Difference spectrometer of a spectrograph is that the
spectrometer is a visual surveillance of the spectrum with through the
eyes, and the spectrograph used a method of recording the spectrum -
plate, recorder, photomultiplier or photocell, digital camera, etc. Both
are used for the rapid qualitative spectral analysis of substances in
chemistry, metallurgy (eg steeloscope) and m . g).
Dispersion of light is called normal if the refractive index decreases monotonically with increasing wavelength (with increasing frequency).
In the case of dispersion if
dispersion of light is called anomalous.
Normal dispersion of light seen in the distance from their own absorption lines, anomalous - within the lines or absorption lines.
spektrosensitometra ISP-73: 1 - source of light (incandescent tungsten
ribbon lamp), 2 - two-lens condenser 3 - disc shutter speeds of 0.05,
0.2 and 1.0 seconds, 4 - revolving disk with a set of perforated
diaphragm; 5 - entrance slit of a spectrograph, 6 - collimator lens 7 -
prism, 8 - the camera spectrograph. (Source: BSE).
To study the normal and anomalous dispersion method can be used crossed prisms.
P1 - glass, P2 - from material dispersion which investigated. If the
prism P2 would not have been on the screen E would be observed range
of normal dispersion glass (Fig. 1). In the presence of the prism P2 is
the curvature of the dispersion pattern at normal dispersion in P2,
and the gap curved dispersion pattern - with anomalous dispersion.
The method of
crossed prisms can not be used in the event that we are interested in n
gas emission, whose refractive index is close to 1. In this case,
D.S. Rozhdestvensky suggested that instead of a prism P1 put Jamin
interferometer, one arm of which is placed a sealed tube with gas, in
another - the plate, whose variance is known. Instead of a prism or
diffraction P2 put prismatic spectrograph ( - diffraction spectrum depends linearly on λ).
§ 2 The electron theory of dispersion of light.
Anomalous and normal dispersion of light. Relationship dispersion and absorption
Macroscopic Maxwell's theory can not explain the dispersion of light. From Maxwell's theory that
, with μ = 1
For water, ε = 81, therefore , in reality nw = 1.33. Such a contradiction between Maxwell's theory and experiment is due to the fact that we correctly apply the formula ε0 = 81, which is valid only in a static field (ω =
0). Water molecules are constantly oriented in alternating electric
field. The electric field of the light wave changes harmonically
ε(ω) < ε(0), поэтому n(ω) < n(0).
Ie for each frequency will have its refractive index. Therefore, we
must take into account the dependence of n on the frequency.
phenomenon of dispersion can be explained by considering the
interaction of light waves with matter. This was made possible thanks
to the classical electron theory of Lorentz.
According to the classical electron theory of electrons in atoms
vibrate under the influence of the quasi-elastic force. Light wave
incident on a dielectric causes the electrons in an atom of the
dielectric to make the forced oscillations with a frequency equal to
the frequency of the driving force. But electrons moving rapidly
radiate electromagnetic waves. These secondary waves emitted by
electrons of the atoms of matter, have the same frequency as the
incident wave. The initial phase may vary. These secondary waves
interfere with the incident wave and the material covered in the
resultant wave whose direction coincides with the direction of the
incident wave, the rate of which depends on the frequency (and in vacuum
equal to the speed of light). Therefore, the refractive index n
depends on the frequency ω.
where χ - the dielectric susceptibility of the medium, P - polarization vector (the resultant dipole moment per unit volume).
According to Maxwell's theory
with μ = 1.
when the substance of the incident light wave, the electric field is
changing so rapidly that the polarizability (we need only electrons,
ie, the induced field of the light wave) does not have time to change
over the field. In this case
where n0 - the number of atoms per unit volume, PE
- induced dipole moment of a single atom. It can be shown that the
the highest exposures of the electric field of the light waves are
more weakly associated with the core electrons, so-called optical
electrons. For simplicity, we assume that each atom contains one optical
х - offset .
n depends on the displacement of electrons in the atom, the field of
the light wave. On an electron in an atom acts as the forces:
quasielastic - because of the presence of the electron with the nucleus:
The driving force of the light wave
Under action of these forces electron begins a forced oscillation
For simplicity we neglect the damping of oscillations. In this case,
The last formula shows that n is dependent on the frequency of the incident light, as well as ε. If ω0> ω, then there is n, if ω0 = ω, then n has a discontinuity of the 2nd kind. In that case, if the atom has several valence electrons:
If we consider the damping (β ≠ 0), then we get a formula which gives a good agreement with the experimental curve)
§ 3 The absorption of light.
the Bouguer law
It was established experimentally
that the light passes through a substance is absorbed. Particularly
strong absorption was observed for the wavelengths, frequencies
coincide with the natural frequencies for the substance. The intensity of light varies as:
where α - absorption coefficient,
I0 - intensity of the incident light,
The thickness of the absorbing layer.
The minus sign indicates that the dI and иhave opposite signs, that is with increasing thickness of the absorbing layer of the transmitted light intensity decreases.
the Bouguer law
The absorption coefficient α
is the value of the inverse value of the way in this matter, which is
going through, the light decreases in intensity by a factor e.
If the solution is
light-absorbing material in a solvent which does not absorb the color,
the absorption coefficient of the solution is directly proportional to
the length of the absorbing material, ie
gas absorption spectrum is ruled. For the gas in the molecular state
absorption spectrum is striped. For solid dielectric absorption
spectrum of the solid in a certain range of frequencies. All other frequencies will pass the dielectric.