A geometric algebra reformulation of geometric optics

Quirino Jr Mallorca Sugon, Daniel J. McNamara

    研究成果: Contribution to journalArticle査読

    8 被引用数 (Scopus)

    抄録

    We present a tutorial on the Clifford (geometric) algebra Cl3,0 and use it to reformulate the laws of geometric optics. This algebra is essentially a Pauli algebra, with the Pauli sigma matrices interpreted as unit rays or vectors. In this algebra, the exponentials of imaginary vectors act as vector rotation operators. This property lets us rewrite the laws of reflection and refraction of light in geometric optics in exponential form. The reformulated laws allow easy translation of symbols to words and to diagrams. They also are shown to be equivalent to standard vector formulations. These coordinate-free laws can be shown to simplify the analysis of geometric optics problems such as the tracing of meridional and skew rays in lenses and optical fibers.

    本文言語英語
    ページ(範囲)92-97
    ページ数6
    ジャーナルAmerican Journal of Physics
    72
    1
    DOI
    出版ステータス出版済み - 1 1 2004

    All Science Journal Classification (ASJC) codes

    • 物理学および天文学(全般)

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