JOURNAL OF COSMETIC SCIENCE 328 fi ber with lower ellipticities changed more dramatically in Figure 6, when the fi ber was rotated around its axis. These facts suggest that the cross-sectional shapes of the fi bers have very signifi cant effects on the refl ection properties. Refl ection curves of hair fi ber measured by goniophotometry generally consist of the following two features: specular refl ections from the front and back surfaces of the fi ber and scattering from the surface and inner parts of the fi ber (5). In the coplanar arrange- ment, specular refl ection from the front surface of a fi ber provides a single peak at the angle deviated from the incident angle due to the inclination angle of cuticles, ca. 2.5 degrees. Meanwhile, in the normal arrangement, refl ections from the front surface of a fi ber radiate over a wide range of angles and never yield peaks in the intensity-vs-receiving- angle curves in the range of the receiving angle, θ, from 0° to 90°. In order to identify the unknown peaks, intensities of the refl ections from the front surface of a fi ber mea- sured in the normal arrangement (Figure 5) are estimated in the following manner: providing a fi ber has a cylindrical shape, the intensity of specular refl ection from the fi - ber, R⊥(Φ) in the normal arrangement should be identical to that in the coplanar ar- rangement, R//(Φ), at the incident angle Φ (the specular refl ection angle) = 0. R//(Φ) was measured with changing the incident angle, Φ, and R⊥(0) was estimated by extrapola- tion, R//(Φ) as Φ → 0. Figure 7 shows the experimental results of R//(Φ) as a function of the incident angle. The incident angle dependence of the specular refl ection intensity follows Fresnel’s equations. The extrapolation from the higher incident angle regions to 0° provides R//(0) ≈ R⊥(0) ≈ 20 (a.u.). Computer simulations were conducted to understand the behavior of specular refl ection in the normal optical arrangement from a cylindrical surface (where minor axis = major axis, E = 1.0), with a refractive index of n ≈ 1.5. As shown in Figure 8, the refl ection intensity shows a broad maximum centered on the receiving angle θ = 0° in the range of θ from -90° to 90°. From the results of Figures 7 and 8, the value of R⊥(θ) in our ex- perimental setup is expected to be 20 (a.u.), at most, in the range of θ from -90° to +90° in the normal arrangement. Figure 7. Intensity of specular refl ection of a blonde hair fi ber as a function of incident angles, Φ, in the coplanar arrangement. Specular refl ection angles of a hair fi ber generally deviate from incident angles owing to the inclination angle of cuticle surfaces.

MECHANISM FOR HAIR SHINE 329 For further understanding of the front surface refl ection of a fi ber in the normal arrange- ment, refl ection from a dark hair fi ber was measured by goniophotometry. According to the fact that the specular refl ection phenomenon from a front surface of a fi ber is indepen- dent of the color of the fi ber, a goniophotometric curve of a dark fi ber can be a proper indication of the surface refl ection of a fi ber. Figure 9 shows the goniophotometric mea- surement result for a dark hair fi ber under the normal arrangement condition. The ellip- ticity of the fi ber was 0.75. Light penetrating into a dark fi ber is mostly absorbed by melanin granules, and the refl ection from the back surface of a fi ber is hardly able to be detected the refl ection observed in Figure 9 is, therefore, predominantly due to the sur- face refl ection. Actually the intensity-vs-receiving-angle curve of the dark hair (Figure 9) is well explained by the simulation results in Figure 8. As is calculated in Figure 8, the refl ection intensity curve yields no obvious peak and the refl ection intensity decreases monotonically from 0° to +90°. Such a strong refl ection as observed in the blonde hair Figure 8. Calculated intensity of front surface refl ection in the case of a cylinder (ellipticity: 1.0). Figure 9. Refl ection intensity of a dark hair fi ber in the normal arrangement (ellipticity: 0.75).