254 JOURNAL OF COSMETIC SCIENCE or antiperspirant emulsion gels exhibit reduced staining while retaining excellent aes­ thetic attributes and efficacy. The water phase comprises about 75% to 90% of the composition and contains a deodorant or antiperspirant effective amount dissolved therein. The oil phase comprises about 10% to 25% of the composition and contains a silicone oil and silicone emulsifiers. Even though it used refractive index matching methodology in the proprietary disclosure, there is no discussion of detailed physical principles, refractive index, or methodology discussion in the patent. Although refractive index matching is used in the development of cosmetic products, it is mainly a process of trial and error. There is no practical methodology to follow in the discovery of new applications because the physical principle is not well explained. In our exploration of refractive index matching in the formulation of cosmetics, detailed physical principles are revealed and a practical method is developed leading to a series of unique formulations ( 4). Refractive index matching enables chemists to make for­ mulas that cannot be achieved by other methods. Refractive index matching should become a common technique for formulation chemists. EXPERIMENT AL MATERIALS Trade names of materials used in this study are as follows: 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, phenyltri­ methicone, 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, isohexa­ decane, and polysorbate 80 (Simugel EG®, Seppic) hydroxyethylacrylate/sodium acryl­ oyldimethyl taurate copolymer, squalane, and polysorbate 60 (Simugel NS®, Seppic) Cl3-14 isoparaffin (Isopar M®, Exxon Mobil Chemical) and Cll-13 isoparaffin (Isopar L ® , Exxon Mobil Chemical). METHODS Refractive indices (n) were measured with an Atago hand refractometer at 25°C under florescent light. Specific gravities were measured at 25°C with a stainless pycnometer. PHYSICAL PRINCIPLES OPTICAL PROPERTIES Consider a beam of light (monochromatic) transmitted through air and directed onto the surface of a body of water (Figure 1). Some of the light is reflected at the interface

REFRACTIVE INDEX MATCHING 255 Normal Incident ray Reflected ray Interface water I r2 Refracted ray Figure 1. A ray diagram of refraction and reflection showing the angle of incidence, the angle of reflection, and the angle of refraction. between the air and water the remainder enters the water and is transmitted through it. The light is represented with an incident ray, a reflected ray, and a refracted ray. Each ray is oriented with respect to a line called the normal, which is perpendicular to the surface at the point of reflection and refraction. The angle of incidence is r 1 , the angle of reflection is r 1 ', and the angle of refraction is r 2 , all measured relative to the normal as shown. Every transparent material has a property called optical density, which is an inverse measure of the speed of light through the material. Because water has a higher optical density than air, the speed of light is reduced as the light enters the water. The beam of light changes direction abruptly as it enters the water because of the change in speed. This bending of the light ray is called optical refraction. Reflection and refraction are confirmed experimentally to obey two laws: the law of reflection and the law of refraction (5 ). The law of reflection states that a reflected ray lies in the plane of incidence and has an angle of reflection equal to the angle of incidence. This means that The law of refraction states that a refracted ray lies in the plane of incidence and has an angle of refraction related to the angle of incidence by . . n 2 sin r2 = n 1 sin r 1 Each of the symbols n 2 and n 1 is a dimensionless constant called the index of refraction or the refractive index (RI). It is defined as the ratio of the speed of light in a vacuum to its speed in a substance (n = clv1 where v is the speed of light in that substance and c is the speed of light in a vacuum). The equation was designated as Snell's Law. The index of refraction of a homogeneous substance is a constant and definite physical property. Consequently, the refractive index can be used to identify a substance, to measure its purity, and to determine the concentration of one substance dissolved in another. Typically, a refractometer is used to determine the refractive index. Some indices of refraction for common cosmetic ingredients are listed in Table I.