HAIR APPEARANCE AND INTERNAL STRUCTURE 399 because of the lack of cuticle structure, the artificial hair shows the apparent colored single reflection resulting from the overlap of the front and back surface reflections. The appearance of metal, such as gold and copper, is characterized by an intense reflec- tion of its own color, which is due to properties of interaction between the free electrons of metals and light in the visible region. The nylon tress shows an intense light reflection due to its smooth fiber surface and a colored single reflection due to an overlap of the surface and back surface reflections, satisfying the conditions to give a metallic appear- ance. The nylon fibers are, therefore, not perceived as an impression along with trans- parency in the macroscopic evaluation, although the fibers are transparent in a micro- scopic view such as Figure l a. INFLUECE OF HAIRSTYLE AND MOTION ON VISUAL APPEARANCE The visual angle between the front and back surface reflections depends greatly on hair curvature, i.e., hairstyle (Figure 6). Figure 10a shows the visual angle calculated as a function of the curvature of a model plate with a spherical light source of a finite size. The calculation conditions are shown in Figure 10b. This geometrical condition (Figure 10b) is the same as that for the photographic conditions of Figure 6. The solid lines with a grayish region and the dotted lines with a horizontal stripe in Figure 10a show the visual angle of the front and back surface reflections against the center of the front surface reflection of a spherical light source. Vertical arrows in the grayish and striped 10a) -30 -20 • -lO o IO -0.05 /• Back surface Front s•a• reflection 20 -0.10 0.00 0.05 0.10 (Concave Form) Curl Curvature / cm 4 (Convex Form) lob) Geometrical condition .for the calculation Angle of surface Light source: .• ...... !..n..c. lin.e.• 2.5ø diameter •x•40 cm •' ....... -" Thickness: -• \ 0.0m cuRr• øt "'" •(•c•4VVisuaangl radius t •••••ø• Point Aj•.j Jucm point Tip Curl curvature = 1 / (Curl radius) Figure 10. (a) Curl curvature dependence of the calculated visual angle of the model plate. (b) Geometrical condition for the calculations. The vertical axis in (a) shows the visual angle against the center of the front surface reflection of a spherical light source. The horizontal axis is the curl curvature of the model plate defined in (b). Solid lines in the grayish region and the dotted lines with a horizontal stripe show the visual angles of the front and back surface reflections, respectively. Vertical arrows in the grayish and striped areas indicate the direction and size of the reflected image of the light source. A positive value in the visual angle means that the back surface reflection is located at the lower side of the front surface reflection. In the geometrical condition for the calculation, the following seven parameters are fixed, as in (b): (1) The refractive indexes of the model plate and the surrounding media are 1.5 and 1.0, respectively. (2) The distance between the viewpoint and the model plate (viewpoint to point A in the figure) is 30 cm. (3) The distance from the light source to point A is 100 cm. (4) The angle between the (2) and (3) above at point A is 45 degrees. (5) The thickness of the model plate is 0.01 cm. (6) The angle of surface incline: Os = 2.5 degrees. (7) The diameter of the spherical light source is 10 cm.

400 JOURNAL OF COSMETIC SCIENCE areas indicate the size and direction of the reflected image of the light source. The arrows correspond to an arrow in the light source shown in Figure 10b. When the model plate is of a convex form, the back surface reflection is located on the upper side of the front surface reflection, as in Figure 10a (more root end side in Figure 10b). This situation corresponds to the hair appearance at the curl curvature 0 in Figure 6. On the other hand, when the model plate is transformed from the convex to concave form, the location of the back surface reflection is moved to the opposite lower side (tip side) of the front surface reflection (curl curvature -0.02 in Figure 6). The size and direction of the reflected image of the light source also greatly depend on the curvature. During the change in the curvature of the model plate from positive (convex form) to negative (concave form), the reflected image is enlarged at first, divergent once in the middle of the process, and then reversed. That is, the relative position and size of the double reflections are dramatically and dynamically moved during the course of hair movement. This optical phenomenon is essentially the same as the reflection behavior observed in a rounded mirror. The symmetrical center of the optical phenomena is not observed at the curvature = 0, but observed at the curvature = -0.02, under the conditions shown in Figure 10b. These kinetic changes of the double reflections, as shown in Figure 6, must cause dramatic and dynamic changes in color and the impression of depth along with trans- parent appearance, leading to brilliant and vibrant impressions in the case of the poreless hair with cuticle structure. In the present study, the influence of the multiple optical interactions among the fibers is not considered, because of difficulties in the calculation. The present simple model, however, reasonably reproduces the optical behaviors of the front and back surface reflections in the actual appearance of the hair tresses, showing that the simple model is valid as a primary approximation for the present study. CONCLUSION It is suggested on the basis of our results that lustrous and colorful appearance, and the impression of depth along with transparency and vibrancy of hair, are achieved by meeting the following three conditions: 1. Poreless structure in the internal hair fiber, Due to the lack of lightscattering origins, the poreless structure allows the visible light to reach and reflect from the back surface, to be observed as an intensive and colored reflection together with surface reflection to give a higher contrast in lightness and saturation of hair color. 2. Well-ordered cuticle structure on the surface of hair fiber. A well-ordered cuticle structure leads to sharp reflections from front and back surfaces and also leads to separation of the two reflections by the inclined cuticle structure. These separated double reflections cause an overestimation of real depth or confusion in our depth perception as a kind of visual illusion, and lead to the impression of depth along with transparency. 3. Proper hair curvature and motion of the hair. Change in tress curvature and motion leads to dramatic and dynamic changes in color perception and the impression of depth along with transparency, leading to a more vibrant appearance. By fulfilling these conditions, the hair looks beautiful: lustrous, colorful, deep along with apparent transparency, brilliant, and vibrant in appearance.