Topics in Particle and Dispersion Science

Scattering vector and phase delay for a tenuous particle

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Fig. 2. Scattering vector and phase delay for light scattering by a tenuous particle. The refractive index, m' of such a particle is close to that of the surrounding medium. Consider scattering of a plane wave with the wavelength λ₀ in vacuum, incident horizontally from the left, by two arbitrarily selected volume elements P and P ' of the particle. Angle θ is the scattering angle. The vector diagram on the right illustrates the relationship, k_s = k_i + q, between the wave vector, k_i, of the incident wave, that of the scattered wave, k_s, and the scattering vector q. We consider elastic scattering, hence | k_s | = | k_i |.
As in Fig. 1, the phase delay, Δφ, between the waves scattered by these volume elements is a product kΔr of the magnitude, k, of the wave vector, k_i , i.e. 2πm' / λ₀, and the geometrical path difference Δr = dr₁ + dr₂ between paths APB and A'P'B'. In contrast to Fig. 1, m' now represents the refractive index of the particle material. In vector notation, Δr = -r • u_s + r • u_i = -r • ( u_s - u_i ). Since, k = ku, it follows that Δφ = -r • q.

CITATION: Jonasz M. 2006. Scattering vector (www.tpdsci.com/Tpc/ScaVctSgnf.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 15-Jun-2006 Modified: 18-Feb-2008 Peer-reviewed: PENDING

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