Geometrical Optics
 作者： Sijiong Zhang ,  Changwei Li ,  Shun Li 出版社： SPIE PRESS,   2017 ISBN： 9781510608368 来源数据库： SPIE-the International Society for Optical Engineering DOI： 10.1117/3.2267707.ch2 原始语种摘要： Geometrical optics, an old branch of optics, formulates optical laws in the language of geometry under the approximation that the scale of the wavelength of light, compared with that of the optical system on which light is incident, is close to zero. In the regime of geometrical optics, a fundamental concept is the optical ray. The feasibility of optical rays introduced in geometrical optics can be explained by quantum theory. According to the uncertainty principle in quantum theory, we cannot simultaneously measure the position ( x , representing a position in the vertical direction) and the momentum ( p , representing a momentum in the vertical direction) of a photon with arbitrarily high precision. The uncertainties of its position and momentum are in compliance with the uncertainty... inequality, Δ x Δ p x ≥ h / 4 &pgr; , where h is Planck’s constant, Δ x is the uncertainty of the position of the photon, and Δ px is the uncertainty of the momentum of the photon. As shown in Fig. 2.1, photons are emitting from a source at an infinite distance, so all of these photons have a momentum of p = h /λ (λ is the wavelength of photons) only in the horizontal direction before passing through the slit or an optical element. After passing through the slit, photons spread out at an angle of Δθ, as shown in Fig. 2.1(a). So the uncertainty of the momentum in the vertical direction can be calculated as Δ px = p Δθ=( h /λ)Δθ, as expressed in Ref. 1. On substituting this expression into the uncertainty inequality equation above, the angle of spread satisfies Δθ ≥ λ/(4&pgr;Δ x ). Here, Δ x is on the order of magnitude of the width of the slit. When λ/(Δ x ) → 0, as shown in Fig. 2.1(b), the angle of spread is close to zero. This means that if the size of the slit (or apertures, lenses, etc.) shown in Fig. 2.1 is much larger than the scale of the wavelength, photons will not spread after passing through the optical element; i.e., propagation paths of photons can be approximated by straight lines. Therefore, it can be concluded that rays traveling in straight lines (in geometrical optics) is an inevitable result of quantum theory when the size of the slit (or apertures, lenses, etc.) is much larger than the scale of the wavelength.

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• uncertainty　不定
• momentum　动量
• passing　通过的
• inequality　不等式