JOURNAL OF COSMETIC SCIENCE 330 (Figure 5) is not observed in the case of the dark hair fi ber. Comparison of the results with blonde hair in relation to those with dark hair suggests that the strong refl ection observed in Figure 5 is not the specular refl ection from the front surface of the fi ber but results from the refl ection from the back surface of the fi ber. From the drastic change in refl ection intensity by a fi ber rotating around the fi ber axis (Figure 6), it was suggested that this change was caused by a structural parameter of the fi ber related to the axial asymmetricity, i.e., the elliptical fi gure of a fi ber cross section. Light path simulations were performed to understand the behaviors of refl ection, refrac- tion, and transmission of the fi ber in the normal optical arrangement. It was assumed in the simulation that the medium surrounding a fi ber is air (n = 1.0), and that the fi ber is elliptical with an ellipticity, E, of 0.5 and a refractive index, n = 1.5. The simulation re- sults are shown in Figure 10, where the direction angle of the ellipse, φ (direction angle: the angle between the major axis of the ellipse cross section and the incident light) is 45°. Three types of rays were separatelty examined: refl ection light from the front surface of the cylinder (front surface refl ection), refl ection light from the back surface (back surface refl ection), and transmission light passing through both the front surface and the back surface of the fi ber (back surface transmission light). It is revealed in back surface refl ection that there are areas at the back surface where light doesn’t transmit at all but is totally refl ected (circled areas in Figure 10). Total refl ection is an optical phenomenon where all of the light striking a medium boundary (from a less optically dense medium to a denser medium with a shallow enough angle) is totally re- fl ected and no light passes through the boundary. The phenomenon is well known as the key mechanism of an optical fi ber for light energy transmission over long distances. The critical angle, θc, is defi ned as the angle of incidence above which total refl ection phe- nomenon occurs, and assigning 90° to the refraction angle, the angle θc is given by Snell’s law. sinθA/sinθB = nB/nA (1) where θA is the incident angle from medium A to medium B θB is the refraction angle nA is the refractive index of medium A and nB is the refractive index of medium B. For fi ber interior (n = 1.5) to air (n = 1.0) refl ection, total refl ection is expected to occur at an incident angle of 41.8° or above, by Snell’s law. Optical confi gurations giving rise to total refl ection are realized only when a cross-sectional fi gure of a fi ber is distorted from a per- fect circle, as is found for an ellipse. Thus, the strong shine observed in Group A is veri- fi ed to be total refl ection. Figure 10. Light path simulation with the direction angle, φ = 45°. The incident light is irradiated from the left side of the fi gure.

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.