MECHANISM FOR HAIR SHINE 333 ray-tracing method. The ratio approximates the proportion of occurrence of total refl ec- tion at the back surface in the total incident light. Refl ectance at the surface and such higher order events as a secondary refl ection inside a fi ber are not taken into account in this simulation. It is shown in Figure 13 that the proportion of total refl ection light depends not only on ellipticity but also on the direction angle, φ. The results show that the proportion of total refl ection occurrence gets smaller with the increase in ellipticity and that total refl ection never occurs with an ellipticity of 1.0. On the other hand, the proportion tends to get larger as φ increases. Figure 14 shows the ellipticity dependence of the proportions of total refl ection based on the results in Figure 13. In this case, the proportion of total refl ection at each ellipticity was calculated as the averaged value over the range of the direction angle of the cross- sectional ellipse from φ = 0° to 90°. In the simulation, different refractive indices were calculated because most of the components of hair-care products have a lower refractive index than that of cuticle (n = 1.54). As a result of the simulation, the proportion in- creases monotonically as the ellipticity decreases, and the proportion also increases with the increase in the refractive index of the fi ber. The lower the refractive index is, the smaller the proportion of total refl ection is. This result also suggests that most organic materials may reduce the proportion of total refl ection. Figure 15 visually shows the total refl ection phenomenon of a real hair fi ber in compari- son with the front surface refl ection. A single blonde fi ber with an ellipticity of around 0.63 was irradiated with white light. The white refl ection line at the edge of the fi ber is the front surface refl ection. The very strong yellowish light observable at the opposite side of the fi ber is predominantly due to the total refl ection light from the back surface of the fi ber. It should be noted that the total refl ection, as well as the condensed light, is to be accompanied by the color of melanin, because the light passes through the interior portion of the fi ber. Melanin also attenuates light traveling inside a fi ber so that the total refl ection can be perceivable as strong rays only when the hair has a lighter color such as blonde. On the other hand, absorption by darker hairs (from brown to black) is supposed to be too large even for the total refl ection to let out (for example, Figure 9). In order to exhibit visually these optical phenomena, transparent acrylic elliptic models, colored pale yellow (n = 1.50), were irradiated with white light. The light was irradiated Figure 14. Ellipticity dependence of the proportions of total refl ection calculated, based on the results in Figure 13. The proportion of total refl ection at each ellipticity was obtained as the averaged value over the range of the direction angle of the cross-sectional ellipse, 0° ≤ φ ≤ 90°.

JOURNAL OF COSMETIC SCIENCE 334 from the left side in Figure 16, and the acrylic model was rotated from φ = 0° to 90°. It is worth noting again that both the total refl ection and the condensed light were observed as strong and sharp rays colored yellow. Figure 16. Acrylic model simulation results (ellipticity: 0.7). The incident light is irradiated from the left side of each fi gure, and the direction angle, φ, is rotated by 30 degrees from (a) 0 to (d) 90 degrees. IL: inci- dent light. TR: total refl ection. LC: light condensation. Figure 15. (a) Photographed image of a blonde hair fi ber. (b) Schematic illustrations of (i) surface refl ection and (ii) back surface refl ection. The back surface refl ection (ii) is virtually due to the total refl ection.