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Wireless Optical Telecommunications by Olivier Bouchet

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Appendix 1

Geometrical Optics, Photometry and Energy Elements

A1.1. Geometrical optics elements

A1.1.1. Refractive index

The refractive index characterizes the ratio of the speed in vacuum (cv) to the speed in another homogeneous environment (ce). In the latter environment, the optical wave propagates at a speed lower than that in vacuum cv. The ratio is expressed by the following equation:

Equation A1.1. Refractive index

Equation A1.1.

Table A1.1 presents some refractive index examples.

Table A1.1. Examples of refractive indexes

Environment Refractive index
Vacuum 1
Air 1.00029
Water 1.3333
Glass 1.5
Diamond 2.41

When the optical wave passes from one environment to another, not only its velocity (speed) but also its trajectory changes. In addition, this index varies with wavelength, which can cause optical aberrations (e.g. the phenomenon of light scattering in a prism).

A1.1.2. Fermat’s principle

Fermat’s principle is the basis for any geometrical optics that describes the refraction and reflection laws. Under this principle, the path followed by a light beam between two points A and B is such that the travel time between these two points is minimum. Then the light propagation is straight in a homogeneous medium with constant velocity (in classical Euclidean geometry). This feature also applies in the context of a path from B to A (principle of light reversibility). ...

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