MECHANISM FOR HAIR SHINE 331 Computer simulation analyses were further performed in order to confi rm the energy distribution of specular refl ection and transmission light in the cross-sectional plane. Calculations were performed under the condition that parallel incident rays were irradi- ated to an elliptic cylinder with a refractive index of n = 1.5 in the normal optical ar- rangement. Examples of the simulation results are shown in Figure 11. As shown in the fi gure, the front surface refl ection spreads radially (Figure 11a), while the back surface refl ection has tendencies both of diffusion or condensation (Figure 11b). The back surface transmission light tends to condense keenly (Figure 11c). The results clearly reaffi rm that a transparent elliptic cylinder acts as a lens. According to the results of the energy distri- bution calculation (Figure 11d), highly directional refl ected light whose intensity is about four times as strong as that of the condensed light is observed in the direction al- most perpendicular to the direction of light condensation. This highly directional refl ec- tion with a very strong intensity is total refl ection. Energy distribution changes by the change in the ellipticity, E, and the direction angle, φ, are illustrated in Figure 12. These simulation results show that the intensity and the angle of the intense refl ection change drastically. Highly directional light can be classifi ed into the following two kinds of light: the light attributed to the total refl ection effect (back surface refl ection light) and the light resulting from the condensation effect of a lens (back surface transmission light). The total refl ection light tends to refl ect back in the direction of the light source when the ellipticity is larger than about 0.6. On the other Figure 11. Light path simulation with the ellipticity, E = 0.5, and the direction angle, φ = 45 degrees. (a) Refl ection from the front surface. (b) Refl ection from the back surface. (c) Transmission light. (d) Resultant energy distribution. The incident light is irradiated from the left side of each fi gure.

JOURNAL OF COSMETIC SCIENCE 332 hand, the total refl ection light tends to be directed toward the opposite side of the light source as the ellipticity increases above 0.6. When the ellipticity was around 0.9 or above, the highly directional light was refl ected back toward the light source side, but its inten- sity was dramatically weakened with the increase in ellipticity. These results satisfactorily explain the tendency of the experimental results in Figures 5 and 6. The total refl ection effect is to be widely perceived in appearance because the typical ellipticity of Caucasian hair is distributed around 0.7 (14) and the effect is suggested to play a signifi cant role on the blonde shine. The highly directional light caused by the condensation effect of the lens function (back surface transmission) emerges on the opposite side of the light source, and the intensity varies in a complex manner. Figure 13 shows the contour map of a number ratio of total refl ection rays out of inci- dent light fl ux as a function of ellipticity and the angle φ (0° ≤ φ ≤ 90°) obtained by the Figure 12. Energy distribution change with variations in the ellipticity, E, and the direction angle, φ. The incident light is irradiated from the left side of each fi gure. Figure 13. Contour map of a number ratio of total refl ection rays out of incident light fl ux calculated by the ray-tracing method. Refl ectance at the surface and such higher order events as a secondary refl ection occur- ring inside a fi ber are not taken into account in this simulation.