# Impact of Fat Content and Lactose Presence on Refractive Index in Different Types of Cow Milk
## 1 Introduction  
The exploration of the optical properties of a medium is deeply rooted in the meticulous analysis of its refractive index, a fundamental parameter that indicates the extent to which the speed of light is delayed upon passing through the medium [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. This significant parameter is a cornerstone in understanding how light interacts with and traverses through various mediums. To facilitate precise measurements, it is necessary to consider a configuration based on internal reflection, which is strategically utilized to determine the critical angle associated with total internal reflection accurately. The internal reflection configuration occurs when the refractive index of the first medium is greater than that of the second propagation medium. Within this setup, it is firmly established that the angle at which light reflects is equal to the angle at which it is incident, a phenomenon commonly referred to as specular reflection [11]. Optical, easily applicable techniques bear considerable significance, offering the community accessible methods applicable across diverse areas and industries. That is why the experiment presented in this manuscript relies on applying [PERSON]'s law and Fresnel coefficients. [PERSON]'s law is a relationship that describes how light refracts as it passes through a flat interface. Fresnel coefficients represent the proportion of incident light reflected and transmitted at the interface between two media with different refractive indices or interfaces [4, 12]. It is important to mention that the most fundamental concept in this work is optical reflectance, defined by the square magnitude of Fresnel coefficients, which is meticulouslyexamined for both \(s\) and \(p\) polarizations [13; 14]. Polarization \(s\) refers to isolating a single component of the electric field perpendicular to the plane of incidence. In contrast, the \(p\) polarization occurs when the electric field is parallel to the plane of incidence [1; 2]. As already mentioned, the total internal reflection plays a crucial role in the experiment, representing a fundamental optical phenomenon wherein all incident light is reflected beyond a specific angle of incidence known as the critical angle [1; 3; 4; 5; 6; 7; 8; 15]. In the pursuit of obtaining comprehensive optical parameters for complex samples, it becomes imperative to explore and integrate various theoretical frameworks that elucidate the intricate interactions between light and the sample under investigation, as exemplified in the case of different types of cow's milk [1; 2; 3; 13; 14]. Among these theoretical models, the effective medium theory (E.M.T.) stands out, offering a conceptual framework to describe complex samples such as particles immersed in a homogeneous medium, assigning them an effective refractive index. By amalgamating the E.M.T. with Fresnel coefficients, researchers are equipped with a simplified yet powerful technique to characterize a diverse array of samples with relative ease [3; 16]. Another optical phenomenon that merits attention, albeit less common, is extinction, which encapsulates the absorption or scattering of light within the sample. This intricate behavior is aptly modeled using the extinction coefficient derived from the venerable Beer-Lambert law. It is imperative to underscore that the sample's refractive index is inherently complex and wavelength-dependent, as elucidated by extensive research [4; 17; 18; 19; 20; 21]. In summary, this research endeavors to comprehensively explore and illustrate various optical properties of the sample under scrutiny, ranging from determining critical angles to studying extinction phenomena. Meticulous experimentation and analysis provide a thorough understanding of the sample's response to light across a spectrum of conditions and angles of incidence.