398 JOURNAL OF COSMETIC SCIENCE 8a) Light ('• r '•x View point SOU ce % Reflection from Refiecti/onfrom• Apparent Depth 8b) Light (-•_ source '-•'- • view point 'N", Reflection from ,-N•'".,, Back surface • •) ffl •'""... d .• Visual Reflection from X '•'"- • .f angle Tip ß , Root Apparent Depth ,.' Figure 8. Model illustration to understand light loci from light source to viewpoint via reflections at the front and back surfaces of an object. (a) Thin model with flat surface, and (b) thin model with inclined surface, compared with the models in Figure 7. The inclined surface in (b) corresponds to the cuticle structure of human hair. 9a) 30 • 20 x• Os --_-2.5 degree • Os = 0.0 degree _ • / 0,, o , " 10 ' t .............. • .............. • ............... • ............ 20 ............................................ 0.001 0.01 0.1 1 10 100 • Thickess / cm Order of hair-thic•ess 9b) Geometrical condition for the calculation Light r-• source"•...... Visual \• .... angle.' ! ....................... • ""'. ,.,: 8v . iAngleof } •'"-..Oo , View }surface i \ •".,..,..0.% •,•... point i incline: : \ 5" ...... ..,, • Model Plate \ • ntcgness Point A Figure 9. (a) Thickness dependence of the calculated visual angle of the model plate described in Figure 8. (b) Geometrical condition for the calculations. The vertical axis in (a) shows the visual angles of the back surface reflection against the front surface reflection. The horizontal axis is the thickness of the model plate. The solid lines with closed circles and open circles, and the dotted line with closed circles, in Figure (a) are for Os = -2.5 degrees, 0.0 degree, and 2.5 degrees, respectively, where Os is the angle of surface incline defined in (b). In the geometrical condition for the calculation, the following four 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 (2) and (3) above at point A is 45 degrees. for inclined surfaces (0s = 2.5 or -2.5 degrees), however, it stays at a finite value even in the extremely thin region. In the case of human hair showing clear double reflections, the impression of depth along with transparency is perceived, as described in the previous section. On the other hand,

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.