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This lecture introduces the 2x2 transfer matrix for optical systems, focusing on the paraxial approximation and the response characterization using height and angle parameters. It covers the passage through interfaces, thin lenses, and spherical mirrors, explaining the transfer matrices for systems like camera lenses. The concept of magnification, focal lengths, and diopters in lens systems is discussed, along with the role of entrance pupils, diaphragms, and chief rays in optical systems. The lecture also addresses the numerical aperture, vignetting effects, and the focal ratio in complex optical systems.