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Conic constant

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17: 441: 365: 264: 175: 85: 180: 482: 422: 107: 501: 51: 271: 511: 475: 94: 414: 516: 506: 468: 345: 366:"The 100th birthday of the conic constant and Schwarzschild's revolutionary papers in optics" 377: 101: 364:
Rakich, Andrew (2005-08-18). Sasian, Jose M; Koshel, R. John; Juergens, Richard C (eds.).
348:
is valid, the optical surface can be treated as a spherical surface with the same radius.
8: 456: 381: 393: 37: 418: 397: 385: 311: 285: 289: 452: 495: 41: 334: 323: 389: 448: 25: 16: 259:{\displaystyle x={\dfrac {y^{2}}{R+{\sqrt {R^{2}-(K+1)y^{2}}}}}} 440: 300: 376:. International Society for Optics and Photonics: 587501. 191: 183: 110: 54: 370:Novel Optical Systems Design and Optimization VIII 258: 169: 100:The equation for a conic section with apex at the 79: 493: 476: 483: 469: 20:An illustration of various conic constants 44:, and is represented by the letter  15: 494: 363: 344:) lens and mirror surfaces. When the 170:{\displaystyle y^{2}-2Rx+(K+1)x^{2}=0} 408: 435: 13: 411:Modern Optical Engineering, 4th ed 14: 528: 439: 357: 237: 225: 148: 136: 1: 351: 104:and tangent to the y axis is 455:. You can help Knowledge by 284:This formulation is used in 48:. The constant is given by 7: 40:) is a quantity describing 10: 533: 434: 409:Smith, Warren J. (2008). 80:{\displaystyle K=-e^{2},} 415:McGraw-Hill Professional 502:Mathematical constants 346:paraxial approximation 260: 171: 97:of the conic section. 81: 34:Schwarzschild constant 21: 261: 172: 82: 19: 417:. pp. 512–515. 181: 108: 52: 382:2005SPIE.5875....1R 272:radius of curvature 512:Geometrical optics 312:prolate elliptical 256: 254: 167: 77: 38:Karl Schwarzschild 22: 464: 463: 424:978-0-07-147687-4 390:10.1117/12.635041 290:oblate elliptical 253: 250: 524: 485: 478: 471: 449:geometry-related 443: 436: 428: 402: 401: 361: 343: 332: 321: 309: 298: 286:geometric optics 280: 265: 263: 262: 257: 255: 252: 251: 249: 248: 221: 220: 211: 202: 201: 192: 176: 174: 173: 168: 160: 159: 120: 119: 92: 86: 84: 83: 78: 73: 72: 532: 531: 527: 526: 525: 523: 522: 521: 492: 491: 490: 489: 432: 425: 405: 362: 358: 354: 338: 327: 315: 304: 293: 275: 244: 240: 216: 212: 210: 203: 197: 193: 190: 182: 179: 178: 155: 151: 115: 111: 109: 106: 105: 88: 68: 64: 53: 50: 49: 12: 11: 5: 530: 520: 519: 517:Geometry stubs 514: 509: 507:Conic sections 504: 488: 487: 480: 473: 465: 462: 461: 444: 430: 429: 423: 404: 403: 355: 353: 350: 247: 243: 239: 236: 233: 230: 227: 224: 219: 215: 209: 206: 200: 196: 189: 186: 166: 163: 158: 154: 150: 147: 144: 141: 138: 135: 132: 129: 126: 123: 118: 114: 76: 71: 67: 63: 60: 57: 42:conic sections 30:conic constant 9: 6: 4: 3: 2: 529: 518: 515: 513: 510: 508: 505: 503: 500: 499: 497: 486: 481: 479: 474: 472: 467: 466: 460: 458: 454: 451:article is a 450: 445: 442: 438: 437: 433: 426: 420: 416: 412: 407: 406: 399: 395: 391: 387: 383: 379: 375: 371: 367: 360: 356: 349: 347: 341: 336: 330: 325: 319: 313: 307: 302: 296: 291: 287: 282: 278: 273: 269: 245: 241: 234: 231: 228: 222: 217: 213: 207: 204: 198: 194: 187: 184: 164: 161: 156: 152: 145: 142: 139: 133: 130: 127: 124: 121: 116: 112: 103: 98: 96: 91: 74: 69: 65: 61: 58: 55: 47: 43: 39: 35: 31: 27: 18: 457:expanding it 446: 431: 410: 373: 369: 359: 339: 328: 317: 305: 294: 283: 276: 267: 177:alternately 99: 95:eccentricity 89: 45: 33: 29: 23: 288:to specify 496:Categories 352:References 335:hyperbolic 398:119718303 324:parabolic 301:spherical 223:− 122:− 62:− 274:at  36:, after 26:geometry 378:Bibcode 342:< −1 333:), and 320:> −1 316:0 > 270:is the 93:is the 421:  396:  297:> 0 266:where 102:origin 87:where 28:, the 447:This 394:S2CID 453:stub 419:ISBN 374:5875 331:= −1 32:(or 386:doi 322:), 310:), 308:= 0 299:), 279:= 0 24:In 498:: 413:. 392:. 384:. 372:. 368:. 281:. 484:e 477:t 470:v 459:. 427:. 400:. 388:: 380:: 340:K 337:( 329:K 326:( 318:K 314:( 306:K 303:( 295:K 292:( 277:x 268:R 246:2 242:y 238:) 235:1 232:+ 229:K 226:( 218:2 214:R 208:+ 205:R 199:2 195:y 188:= 185:x 165:0 162:= 157:2 153:x 149:) 146:1 143:+ 140:K 137:( 134:+ 131:x 128:R 125:2 117:2 113:y 90:e 75:, 70:2 66:e 59:= 56:K 46:K

Index

Ten different conic sections which open to the right from a common intersection point, at which point they have a common radius of curvature
geometry
Karl Schwarzschild
conic sections
eccentricity
origin
radius of curvature
geometric optics
oblate elliptical
spherical
prolate elliptical
parabolic
hyperbolic
paraxial approximation
"The 100th birthday of the conic constant and Schwarzschild's revolutionary papers in optics"
Bibcode
2005SPIE.5875....1R
doi
10.1117/12.635041
S2CID
119718303
McGraw-Hill Professional
ISBN
978-0-07-147687-4
Stub icon
geometry-related
stub
expanding it
v
t

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