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Fig.1 shows various sharp maxima as a function of refractive index n of the droplet - for example, the four maxima between n = 1.33 and n = 1.34 are marked by the letters A - D (A and B for perpendicular polarisation, C and D for parallel polarisation). A and C are relatively broad maxima, whereas B and D are extremely narrow. It is interesting to note that the maxima shown in Fig. 1 (and also in the other graphs on this page) tend to occur in pairs - in which a broad maximum (e.g. A) occurs close to a narrow maximum (e.g. B) leading to the observation that A and B (or C and D) seem to be linked in some way.
Fig. 1 shows the maxima occurring as a function of the refractive index n of the droplet. However, Fig. 2 shows that similar patterns occur when intensity is plotted as a function of size parameter x at a fixed value of refractive index n. Fig. 2 consists of five separate graphs (a) - (e) showing results for values of n between 1.33 and 1.334.:
Note that the locations of the maxima seem to be almost independent of the scattering angle θ - as can be seen by comparing Fig. 2(a) for θ = 150° with Fig. 3 for θ = 170°. Although the graphs show different intensities, the maxima A, B and D occur at essentially the same values of size parameter x - but the maximum C seems to disappear as θ increases from 150° to 170°.
Visual inspection of Fig. 2 (a) - (e) suggests that the locations of the maxima A - D move downwards in terms of x as the refractive index n is increased. This behaviour is quantified in Table 1 below:
A | B | C | D | |||||
Refractive index n | x | x * n | x | x * n | x | x * n | x | x * n |
1.33 | 96.744 | 128.6695 | 96.8315 | 128.7859 | 97.0205 | 129.0373 | 97.204 | 129.2813 |
1.331 | 96.6745 | 128.6738 | 96.761 | 128.7889 | 96.9535 | 129.0451 | 97.134 | 129.2854 |
1.332 | 96.6055 | 128.6785 | 96.6905 | 128.7917 | 96.8865 | 129.0578 | 97.0645 | 129.2899 |
1.333 | 96.536 | 128.6823 | 96.62 | 128.7945 | 96.82 | 129.0611 | 96.9955 | 129.295 |
1.334 | 96.4665 | 128.6863 | 96.55 | 128.7977 | 96.7535 | 129.0692 | 96.926 | 129.2993 |
Table 1 Locations of the maxima A, B, C and D as identified in Figs. 2 (a) - (e)
Table 1 shows that the products of x * n for each of the maxima A - D is roughly constant (e.g.maximum A seems to occur when the product x * n ≈ 128.68, whereas B seems to occur when x * n ≈ 128.79). Using these values of the products x * n, we can now identify the maxima A - D in Fig. 4 below which shows a false-colour map of the intensity scattered at θ = 150° as a function of refractive index n of the droplet and its size parameter x.
Although these sharp maxima appear as a function of refractive index n of the droplet and as a function of its size parameter x, it is noteworthy that such maxima do not appear on graphs of intensity as a function of scattering angle θ.
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