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

2. 1 0 1 - 1 f 1 L 0 1 PROPAGATION POSITIVE LENS STRAIGHT INTERFACE CURVED INTERFACE n1n1 n2n2 1 0 0 n1n1 n2n2 R n1n1 n2n2 n1n1 1 0 n2n2 n 1 - Rn 2 n2n2

3. Images and Cavities FF After a round-trip, the image has the same shape and size as the original object 2f 1 1010 y0y0. = y0y0 0101 -1/f. 2f 1 1010. = 2f 1 -1/f. y0y0 -y -1/f = 2f 1 -1/f. 0 = 2f 1 -1/f 0

4. Images and Cavities FF If we follow a single beam that does not pass through the center:: The rays fill the whole area of the sphere. =  y 2N  y y0y0 0101 1 2N/f f

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. “Concentric” configuration: Various equivalent configurations 2f 1 1010. 0 = 2f 1 -1/f -1/f -  /f -2    f -  /f ++ ++ = 00. 00 0 -1/f -  f)  -  f) -  f)