258 JOURNAL OF COSMETIC SCIENCE a surface, such as from air into quartz or vice versa, the blue component bends more than the red component. A beam of white light (or fluorescent light) consists of all (or nearly all) colors in the visible spectrum with near uniform intensity. When white light passes through a solid glass prism with a triangular cross section, all colors of the light are separated into a rainbow. The opalescent appearance of cosmetic emulsions originates from the slight mismatch of the RI between the water and oil phases, which leads to light separation. The opalescent effect has been used to create attractive visual effects in emulsion prod­ ucts. In fact, most clear emulsions created from RI matching appear to be opalescent, more or less due to the difficulty in completely matching RI values. Chemists can utilize equations 4 and 5 to design formulas that meet specific require­ ments of appearance and performance. After the RI of the two phases are matched (become equal) and mixed together, the emulsion may initially be cloudy. A longer mixing time is needed to guarantee emulsion homogeneity and clarity. RES UL TS AND DISCUSSION EXAMPLE APPLICATIONS The following two examples demonstrate refractive index matching. These simplified formulas are intended only to describe the process of formulation design they are by no means the best performing. The chemist can design a multitude of formulas with many different ingredients by using the principles already described (6). This method can also be used to design general dual-phase products with two colors. RI matching in skin-care products: A clear AHA gel. Alpha hydroxy acids (AHAs) have been determined to have antiaging and antiwrinkle effects. AHAs have been widely used in skin-care formulations (7 ,8). However, AHAs are also skin irritants. By incorporating an AHA complex (glycolic acid and arginine) into a water-in-silicone oil emulsion, it is possible to reduce potential irritation and obtain a clear eye-gel product. The following example shows a preliminary formula with the corresponding RI. The related RI cal­ culation is also given for Ri oit (1.3967) and Ri water (1.3966) as an example when using equations 4 and 5. The clear eye-moisturizing gel example is shown in Table II. RI matching in hair-care products: An 0/W hair silicone styling gel. Silicone oil is often used to deliver shine, a luxurious feel, anti-frizziness, and manageability to hair-care products (9,10). Hair fixative ingredients (such as PVP/VA or PVP) are commonly used in carbopol gels, giving styling effects to hair. Interestingly, if one can combine silicone oil and hair fixatives into a clear gel-like product, the new product will impart both hold and the aforementioned properties of silicone. As shown in Table III, the principle of RI matching can be used to make a clear silicone styling gel, with a value of 1.4060 calculated for both the RI0it and the Riwa t e r · DEVIATIONS AND PRACTICAL RI ADJUSTMENT Actual refractive index values often deviate from theoretical values. In theory, calcula­ tions in the summation of the refractive index for solutions apply only to ideal solutions or ideally dilute solutions. In ideal solutions, the molecules of various species are so

REFRACTIVE INDEX MATCHING Table II Clear Eye-Moisturizing Gel Ingredient Silicone oil phase Cyclomethicone and dimethicone (DC 1501, Dow Corning) Cyclomethicone and dimethicone copolyol (DC 5225, Dow Corning) Cyclomethicone (DC 344, Dow Corning) AHA water phase Water, deionized Glycerin Glydant Glycolic acid and arginine (AHCare G-60, Cognis) Rloil = (10 X 1.397 + 10 X 1.398 + 5 X 1.394)/25 = 1.3967. R/wctter = (35.5 X 1.333 + 27 X 1.468 + 12.5 X 1.428)/75 = 1.3966. Table III Weight % 10.0 10.0 5.0 36.1 26.25 0.15 12.5 100.0 Clear Silicone Styling Gel Calculated for Both Oil and Water Phases Ingredient Silicone oil phase Cyclomethicone (Rhodorsil 45V5, Rhodia) Polyacrylamide, C13-14 isoparaffin, and laureth-7 (Sepigel 305, Seppic) Cyclomethicone, phenyltrimethicone, and dimethicone (Gelaid 5565, Chemsil) PVP!VA water phase Water, deionized Glycerin PVP/V A copolymer solution (50% active) (Luviskol VA 73W, BASF) DMDM hydantoin (Glydant, Lonza Group) R/oil = (4 X l.396 + 3 X 1.446 + 20 X 1.402)/27 = 1.4060 R/uwer = (26.5 X 1.333 + 21.35 X 1.472 + 25 X 1.427 + 0.15 X 1.425)/73 = 1.4060 Weight % 4.00 3.00 20.00 26.50 21.35 25.00 0.15 100.00 259 RI value 1.3971 1.3975 1.3942 1.333 1.468 1.425 1.428 RI value 1.396 1.446 1.402 1.333 1.472 1.427 1.425 similar (in terms of structure and spatial filling) to one another that molecules of one component can replace molecules of another component in the solution without chang­ ing the solution's energy or spatial structure. In ideally dilute solutions, all solutes are present in very low concentrations and the solvent weight percentage approaches 100%. In cosmetic formulations, solutions are neither ideal nor ideally dilute because the solvent and solutes cannot be very similar, and the concentrations of solutes cannot be impractically low. They are non-ideal solutions containing both electrolytes and non­ electrolytes. More precise calculations would require chemical potential (µ), solute activity (a), and activity coefficients (-yJ The calculation becomes very complicated and impractical for cosmetic chemists. Fortunately, a simplified calculation is sufficient to serve the purpose of designing formulas. In the process of making the oil phase and water phase, for example, the RI will deviate slightly from the calculated value. The deviation in the oil phase is usually very small because all the RI values of the oil-phase ingredients are very close. Consistent RI