256 JOURNAL OF COSMETIC SCIENCE Table I Refractive Indices (n) of Some Selected Cosmetic Ingredients Water, deionized Glycerin Hexylene glycol Butylene glycol Propylene glycol Ingredient Glycereth-7 (Liponic EG-7, Lipo Chemicals) Glycereth-26 (Liponic EG-1, Lipo Chemicals) PEG-4 (Carbowax PEG 200, Union Carbide) PEG-6 (Carbowax PEG 300, Union Carbide) PPG-9 (Polyglycol P-425, Dow Chemical) PVP/V A copolymer (Luviskol VA 73W, BASF AG) PVP (Luviskol K30, BASF AG) Cyclomethicone and dimethicone (DC 1501, Dow Corning) Cyclomethicone (Rhodorsil 45V5, :Rhodia) Cyclomethicone, phenyltrimethicone, and dimethicone (Gelaid 5565, Chemsil) Cyclomethicone and dimethicone copolyol (DC 5225, Dow Corning) Polyacrylamide, Cl3-14 isoparaffin, and laureth-7 (Sepigel 305, Seppic) Sodium acrylate/acryloyldimethyl taurate copolymer, isohexadecane, and polysorbate 80 (Simugel EG, Seppic) Hydroxyethylacrylate/sodium acryloyldimethyl taurate copolymer, sgualane, and polysorbate 60 (Simugel NS, Seppic) C13-14 isoparaffin (lsopar M, Exxon Mobil Chemical) C 11-13 isoparaffin (lsopar L, Exxon Mobil Chemical) SNELL'S LAW AND REFRACTIVE INDEX MATCHING n 1.3330 1.4680 1.4276 1.4401 1.4355 1.4720 1.4690 1.4582 1.4615 1.4455 1.4275 1.3805 1.3972 1.3960 1.4015 1.3975 1.4460 1.4450 1.4475 1.4380 1.4255 Snell's law states that if n 2 is equal to n 1 , then r 2 is equal to r 1 . In this case, no refraction takes place and the incident beam continues in an undeflected direction. This case applies to cosmetic emulsions when the RI of the oil phase is equal to the RI of the water phase. The resulting emulsion is clear if the indices have been matched properly. In the formulation of cosmetics, this application is referred to as refractive index matching. THEORETICAL DESIGN OF CLEAR EMULSIONS Cosmetic chemists are interested in designing products using the principle of refraction. Experimentally, it turns out that if one mixes several miscible ingredients together to form a clear homogeneous liquid phase, the refractive index of the mixture can be calculated from each individual component's refractive index in the composition (4). The calculated value of the refractive index normally is very close to the value measured instrumentally. If W represents the weight of each component and n represents the refractive index of each component, then the RI of the mixture will be determined by equation 1 and 2, which simplify to equation 3. The calculation equations are: where Rlmix = [Wl X nl + W2 X n2 + W3 X n3 + ... + wn X nn}!Wy (1) (2)

REFRACTIVE INDEX MATCHING We can simplify this equation as: Rlmix = [L(Wi X ni)J/Wy 257 (3) By using equation 3, indices of clear water-phase solutions containing several functional cosmetic ingredients, together with clear oil-phase solutions containing several func­ tional cosmetic ingredients, can be calculated. It is possible to manipulate the refractive index of the water phase to be equal to that of the oil phase. Furthermore, it is possible to make a clear or opalescent emulsion by combining the water phase and the oil phase. In order to use equation 3 directly for refractive index matching in an emulsion, equation 3 is modified, as shown in equation 4 for Rl oit and equation 5 for Rl water : (4) where W i is the weight of each component in the oil phase and n i is the refractive index for each component in the oil phase. (5) where Wi is the weight of each component in the water phase and ni is the refractive index for each component in the water phase. In practice, emulsifiers have to be dissolved in either the oil or the water phase, and so it is necessary that either phase be clear or nearly so. Some limitations have been found when using equations 4 and 5. First, no chemical reactions should take place between ingredients in either the water or the oil phase. Even neutralization will change the refractive index of some ingredients. Second, ingredients in the oil phase should be physically insoluble in the water phase, and vice versa. In another words, the ingredients chosen for use in the formula should not have dual distribution in both the water phase and the oil phase. An emulsifier (or blended emulsifier ingredients) should stay at the interface of its original phase and cannot be allowed to permeate into the other phase. Third, it is necessary to produce emulsions at room temperature because RI values are temperature-dependent and normally the oil phase and the water phase differ in their temperature dependency. If a clear emulsion is obtained at an elevated temperature, the emulsion most likely will be cloudy or hazy at room temperature. The refractive index also varies with the wavelength of light (5 ). Normally literature listed as nD 20 signifies the refractive index using the D-line emission of sodium, mea­ sured at 589 nm at 20°C. RI readings from a refactometer are slightly different from literature values since readings are obtained from the visible range of light (either white light or fluorescent light). With index matching in the development of cosmetic emul­ sions, if the indices of refraction of the water and oil phases are close, but not exact, an opalescent (translucent) appearance will result. This occurs because of light separation caused by a dispersed, drop-like inner phase. The index of refraction n (light bending) encountered by light in any medium except a vacuum depends on the wavelength of the light. The dependence of the refractive index on wavelength implies that when a light beam consists of rays of different wavelengths, the rays will be refracted by a surface at different angles, that is, the light will be spread out by refraction. This spreading of light is called chromatic dispersion. Generally, the index of refraction in a given medium is greater for a shorter wavelength (blue light) than for a longer wavelength (red light). In other words, if a beam consisting of both blue and red light waves is refracted through