# Impact of Fat Content and Lactose Presence on Refractive Index in Different Types of Cow Milk
## 3 Results and Discussion  
All the reflectance data acquired before the calibration, see Figure 2a, are illustrated in Figure 4, showcasing the uncalibrated reflectance density map of the various cow's milk types. Figure 4 is important because it shows the potential of the optical technique. This visual representation offers insights into the reflectance characteristics across different angles of incidence and wavelengths. This manuscript, as shown in Figure 5, focuses on a wavelength of 525 nm. The chosen wavelength was arbitrary when analyzing the optical characteristics at said wavelength, but the experiment allowed us to obtain the same optical parameters at other wavelengths. The discernible abrupt decline in reflectance between the 60- and 65-degree angles of incidence is particularly notable, indicating a significant change in light interaction with the milk samples within this angular range. The optimal wavelength for the reflectance plots employed in this research was determined by scrutinizing these density maps. Figure 3: Sample arrangement. Figure 4: Reflectance density map as a function of angle of incidence (\(20^{\circ}\) to \(75^{\circ}\)) and wavelength for the different types of milk (475 nm to 800 nm). (**a**) Reflectance density map for whole milk; (**b**) reflectance density map for light milk; (**c**) reflectance density map for lactose-free milk; (**d**) reflectance density map for lactose-free light milk. Figure 5: Impact of fat content and lactose presence on light reflectance in milk samples. These graphs are at a fixed wavelength of 525 nm as a function of the angle of incidence, ranging from 20 to 70 degrees. (**a**) Reflectance curve for whole milk; (**b**) Reflectance curve for light milk; (**c**) Reflectance curve for lactose-free milk; (**d**) Reflectance curve for lactose-free light milk. Figure 5 illustrates the various reflectance plots featuring calibrated angular scales for the different types of milk. Within this figure, the most crucial aspect is the presence of two critical angles and the area encompassed between them. It holds significance as it denotes the region where the sample's extinction is evaluated. While the reflectance derivative plots for each milk type are not presented here for the sake of simplicity, it is essential to highlight that such analysis was conducted to determine the real part of each refractive index using [PERSON]'s law Equation (5). This comprehensive approach allows for a deeper understanding of the optical properties of the milk samples and facilitates the extraction of crucial parameters essential for further analysis and interpretation, such as the real part of the refractive index for both interfaces. After acquiring the real part of the refractive index, the theoretical and experimental reflectance versus angle of incidence graphs are generated and presented in Figure 6. These graphs serve as a crucial step in the analysis process, allowing for a comparison between theoretical predictions and empirical observations. By incorporating parameters such as the radius of particle and volume fraction, derived from [PERSON]'s effective medium theory Equation (7), into the analysis, a comprehensive understanding of the optical behavior of the milk samples is achieved. This integration of theoretical models with experimental data enhances the accuracy and reliability of the analysis, enabling researchers to extract meaningful insights into the underlying mechanisms regulating light interaction with the milk samples. Thus, Figure 6 serves as a pivotal visualization tool, facilitating the interpretation and understanding of the behavior of different samples. It is necessary to mention that Figure 6 is not a fitting curve; it is just the simulation and the experiments that match better between both curves. Figure 6: Theoretical and experimental comparison of the milk’s reflectance curves as a function of angle of incidence (20\({}^{\circ}\) to 70\({}^{\circ}\)) and fixed at a wavelength of 525 nm.