Lighting theory refraction

The Rayleigh approximation shows that the intensity of scattered light depends on the wavelength of the light, the refractive index of the system (subject to the limitation already cited), the angle of observation, and the concentration of the solution (which is also restricted to dilute solutions). In the Rayleigh theory, the size and shape of the scatterers (M and B) enter the picture through thermodynamic rather than optical considerations. 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

The abihty of fillers to improve paper brightness increases with their intrinsic brightness, surface area, and refractive index. According to the Mie theory, this abiUty is maximum at an optimum filler particle size, about 0.25 pm in most cases, where the filler particle size is roughly one-half the wavelength of light used for the observation. 

The refractive index of a substance is, of course, a relative expression, as it refers to a second substance, which, in ordinary determinations, is always the air. The term refractive index indicates the ratio of the velocities with which light traverses the two media respectively. This is, as is easily demonstrated by a consideration of the wave theory of light, identical with the ratio of the sine of the angle of incidence, and the sine of the angle of refraction, thus—... 

Theory The initial understanding of the refraction of light dates back to Maxwell s study of electromagnetic radiation. Ernst Abbe invented the first commercial refractometer in 1889 and many refractometers still use essentially the same design. 

Usually, the most general nonspecific effects of dipole-orientational and electronic polarization of the medium are discussed, and the results of the theory of relaxational shifts developed under the approximation of a continuous dielectric medium may be used.(86 88) The shift of the frequency of the emitted light with time is a function of the dielectric constant e0, the refractive index n, and the relaxation time xR ... 

We should first correct the wavevector inside the crystal for the mean refractive index, by multiplying the wavevectors by the mean refractive index (1 + IT). This expression is derived from classical dispersion theory. Equation (4. 18) shows us that is negative, so the wavevector inside the crystal is shorter than that in vacuum (by a few parts in 10 ), in contrast to the behaviom of electrons or optical light. The locus of wavevectors that have this corrected value of k lie on spheres centred on the origin of the reciprocal lattice and at the end of the vector h, as shown in Figure 4.11 (only the circular sections of the spheres are seen in two dimensions). The spheres are in effect the kinematic dispersion surface, and indeed are perfectly correct when the wavevectors are far from the Bragg condition, since if D 0 then the deviation parameter y, 0 from... 

Note that the number of diffraction peaks decreases with time as the droplet diameter decreases, and the number density of peaks is very nearly proportional to the droplet size. The intensity of the scattered light also decreases with size. The resolution of the photodiode array is not adequate to resolve the fine structure that is seen in Fig. 21, but comparison of the phase functions shown in Fig. 22 with Mie theory indicates that the size can be determined to within 1% without taking into account the fine structure. In this case, however, the results are not very sensitive to refractive index. Some information is lost as the price of rapid data acquisition. 

According to scalar diffraction theory (Section 4.4) the scattering amplitude in the forward direction is proportional to the cross-sectional area of the particle, regardless of its shape, and is independent of refractive index. To the extent that diffraction theory is a good approximation, therefore, the radius corresponding to the response of an instrument that collects light scattered near the forward direction by a nonspherical particle is that of a sphere with equal cross-sectional area. The larger the particle, however, the more the... 

At the present time the electromagnetic scattering theory for a sphere, which we have called Mie theory, provides the only practical method for calculating light-scattering properties of finite particles of arbitrary size and refractive index. Clearly, however, many particles of interest are not spheres. It is therefore of considerable importance to know the extent to which Mie theory is applicable to nonspherical particles. To determine this requires generalizing from a large amount of experimental data and calculations. We summarize... 

Newtons theory of refraction was based on the presumed attraction of the particles of transparent bodies for the particles of light passing near them. Since objects containing sulphurous particles (combustibles) have greater power of refraction than other bodies, they must have a greater force of attraction, a proposition Newton supports by citing the fact that the concentrated rays of sunlight attract the sulphurous particles from combustible bodies as flame. 

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