Geometrical Optics

Abstract The theory of geometrical optics as presented here is associated with rays that propagate at small angles where the sine of the angle can be replaced by the angle in radians. This is called the paraxial theory and it fails to describe the actual performance of an optical system. The departures of the paraxial predictions from actual performance are called aberrations, and the various types are introduced: spherical aberration, coma, astigmatism, field curvature, and distortion. Geometrical optics and the concept of total reflection are used to derive a simple theory of guided waves. Some of the basic properties of guided waves are obtained using this simple theory. The Lagrangian formulation of geometrical optics is used to prove that rectilinear propagation is obtained when the propagation medium is homogeneous and to derive the propagation in an optical fiber with an index of refraction that varies in the radial direction.