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This lecture covers the mathematical tools needed to calculate the optical properties of materials, focusing on the complex refractive index which combines refraction and absorption phenomena. It explains how the complex refractive index is related to the speed of light and absorption, and how it can be used to link intensity with electromagnetic wave equations. The lecture also demonstrates the impact of the complex refractive index on light propagation and absorption, and how it influences reflectivity. Additionally, it discusses the relationship between the complex refractive index and absorption coefficient, providing insights into the properties of materials.