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.


v ph



Spectrum shown 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.


Description: Spektrosensitometr ISP-73 (optical system)

Optical scheme 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.

Prism 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.

The 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.

In conditions 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 electron. then


х -  offset .

ie 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:


resistance force:

F resist

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


For sparse 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.


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