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Chapter 3:
Basic Geometric Optics

3.1 Ray Tracing

A ray is a convenient representation of wave propagation. A ray represents the normal to a wavefront. Geometric optics defines the transport of light through simple geometric constructions of ray transmission and reflection. Snell's law is the only consideration during transmission of a ray. Paraxial optics specifies cardinal points without consideration of aberrations. Seidel aberrations indicate defects through polynomials within ray-intercept plots. Comprehension of the ensuing topics is essential for the effective design of an optical instrument.

It is important to remember that geometric optics is a simple model for more complex wave propagation. Ignorance or negligence of physical optics frequently yields a dysfunctional design. Ray tracing is a convenient and powerful tool; however, it is not a complete description of an optical system.

3.2 Cardinal points

There are three cardinal points in a lens: the principal point, the focal point, and the nodal point. These cardinal points are easily managed in systems with identical refractive indices at the object and image. However, the immersion oil of a high-power objective lens requires a more complex set of cardinal points.

The principal point of a lens defines an axial point of refraction by the lens. The principal point of a lens may be extended into a principal plane of the lens or even a principal surface of a spherical shape. All refraction occurs at the principal plane. A lone principal plane defines a thin lens where all rays are bent only at the principal plane. A principal plane may also be split into a front and back principal plane, which is the definition of a thick lens. There is no radial displacement of rays between the principal planes of a thick lens. A thick lens provides a simple description of a complex lens through paraxial optics.

The focal point of a lens defines a point of convergence for incident axial rays. A focal length is defined by the distance from a principal plane to a focal point. If the refractive index of the image is different from the refractive index of the object, then there are two different focal lengths: a front focal length for the incident rays of the object and a back focal length for the exiting rays of the image. The effective focal length (EFL) normally cites the focal length in air.

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