Download e-book for kindle: Applied optics and optical engineering. Vol. I: Light. Its by R. Kingslake

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Example text

Consider the example of road surface mirages. Since the hot air rises, on a hot road surface the air lower down is hotter and less dense than layers above. This is an inversion layer. Throughout the layer the pressure P is roughly constant. We know from thermodynamics that P = constant implies pT = constant where p is the air density. The Gladstone-Dale law states that in a gas the deviation of n from its value in a vacuum is proportional to gas density p : (n-l)a::p Let L be the distance at which rays appear to reflect from the road.

1-2d) O a (cladding) where nl and n2 represent the core and cladding refractive indices respectively, a being the core radius and r = a represents the core-cladding interface. A all (26) Thus x(z) = Asin Fz e-Bcos Fz (27) and similarly y(z) = Csin Fz s-Dcos Fz (28) which represent the rigorously correct ray paths inside the core of a parabolic index fiber. The constants A. B. C and D are determined from the initial launching conditions of the ray; this is indeed very similar to the 2-dimensional harmonic 40 Lagrangian Optics oscillator problem where the trajectory of the oscillator is determined from the initial conditions.

LO) that this is satisfied also for tP = tPo + 1t and r = a2lro. Thus all rays emanating from (ro, tPo) intersect again at (a2lro. tPo + 1t), and the imaging is perfect (Fig. 1). (lO) are circles . 58 Lagrangian Optics y x Fig. 1 Path of rays in Maxwell's fish eye. Loci of constantrefractive index are shown as dashedcircles. Optical Lagrangian and the ray equation for cylindrically symmetric profiles" In the previous chapter we had derived the ray equation (11) where ds represents the arc length along the path of the ray.

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Applied optics and optical engineering. Vol. I: Light. Its generation and modification by R. Kingslake

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