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GEOMETRICAL OPTICS

y a. y’ a ’. A B C D. =. GEOMETRICAL OPTICS. Paraxial approximation: LINEAR OPERATIONS ON RAYS. y. OPTICAL SYSTEM. a ’. y’. a. 1 0 0. 1 L 0 1. 1. -. f. 1 0 1. 1 0. n 1. n 1 -. n 2. n 2. Rn 2. PROPAGATION. STRAIGHT INTERFACE.

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GEOMETRICAL OPTICS

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  1. y a . y’ a’ A B C D = GEOMETRICAL OPTICS Paraxial approximation: LINEAR OPERATIONS ON RAYS y OPTICAL SYSTEM a’ y’ a

  2. 1 0 0 1 L 0 1 1 - f 1 0 1 1 0 n1 n1 - n2 n2 Rn2 PROPAGATION STRAIGHT INTERFACE n2 n1 n1 n2 n2 n1 POSITIVE LENS CURVED INTERFACE R

  3. . y 0 y 0 y 0 1 0 1 0 2f 1 2f 1 = . . -1 -1/f 1 -1/f 2f 1 0 1 . . -1 -1/f 2f 1 -1 -1/f 2f 1 -1 0 0 -1 -y -1/f = = = Images and Cavities F F After a round-trip, the image has the same shape and size as the original object

  4. . Dy 2NDy Dy 0 1 2N/f 0 1 = f Images and Cavities If we follow a single beam that does not pass through the center:: F F The rays fill the whole area of the sphere

  5. “Concentric” configuration: The rays through the center reproduce themselves

  6. “Concentric” configuration: Various equivalent configurations

  7. If the distance between mirrors is larger than twice the radius, The beams “spill over” the mirrors

  8. 0 a -e(2+e/f)a -e(2+e/f) - (1+e/f) - (1+e/f) . . 0 a -1 -1/f -1 -1/f 0 -1 -2e-e2/f 1 0 2f 1 1 -1/f 2f -1 -e/f 0 -1 +e +e = = -e/f -e/f “Concentric” configuration: Various equivalent configurations

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