Geometric optics validity

Naturally this coincidence does not mean that the geometric optics added to the classical physics could be used for the exact description of the light propagation since the Michelson-Morley experiment refuted its validity forever. It is evident that there are possible new mathematical definitions for c+ and c instead of the ordinary speed addition mle of the classical physics seen in Eqs. (9) and (11). These can be compatible with the experimental results as well. 

The variety of results presented can be illustrated by a simple model which treats brightness from the point of view of geometrical optics only.12 The proposed model will be valid if the following assumptions are fulfilled ... 

The interpretation of PDA principles based on geometrical optics is valid only for particles considerably larger than the wavelength and also when only one scattering mode is present on the detector aperture. Extensions can be introduced to account for the Gaussian beam intensity distribution (Sankar and Bachalo 1991). 

The limits zmjn and zmax are the values of defocus at which the reflected rays just fill the area of the transducer thus for zmin < z < zmax all the reflected rays that enter the lens fall on the transducer, while for values of defocus outside that range some of the rays miss it altogether. The value z0 is the defocus at which the geometrically reflected rays are focused on the transducer at this point, as indeed at z = 0, ray optics breaks down because it does not allow for diffraction, although it does correctly predict the position of a minimum in V(z) at z0. The approximate expressions are valid when D/n > q, as is usually the case in a high-resolution acoustic microscope. In the approximation for z0, the quantity Ft is the ratio of the separation between the transducer and the back focal plane of the lens D — q/n) to the Fresnel distance for the transducer (na /Ao),... 

In this context, the refractive index in Eqs. 3.1-2, 3.1-3, and 3.1-6 is assumed to be n = 1, valid for air or vacuum between the optical elements. The optical conductance G = Go in this case is equal to the geometrical conductance Go-... 

The first one is due to the fact that these profiles are optical thickness profiles, with unknown optical index in the craze. Hence, neither geometrical profiles T(x) nor fibril volume fraction Vf(x) distribution in the craze are known. Both are necessary to calculate absolute values of the craze surface stress. As discussed in reference under certain conditions, valid craze surface stresses may be... 

The direct comparison of the results from optical methods with those from aerodynamic methods requires knowledge of the density of the particles to convert the aerodynamic diameter into the geometric diameter. Because of the unknown porosity of the silica agglomerates, no valid conversion was known. Experiments using a direct optical method to measure fractions of aerodynamic classified silica agglomerates [1] led to an effective particle density of a silica agglomerate of about 0.075 g/cm. ... 

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