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phys documents (dragged) 31 - 6.2.3 Principal planes The...

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Chapter 6: Optics 25 D := 1 /f is called the dioptric power of a lens. For a lens with thickness d and diameter D holds to a good approximation: 1 /f = 8( n - 1) d/D 2 . For two lenses placed on a line with distance d holds: 1 f = 1 f 1 + 1 f 2 - d f 1 f 2 In these equations the following signs are being used for refraction at a spherical surface, as is seen by an incoming light ray: Quantity + - R Concave surface Convex surface f Converging lens Diverging lens v Real object Virtual object b Virtual image Real image 6.2.2 Mirrors For images of mirrors holds: 1 f = 1 v + 1 b = 2 R + h 2 2 1 R - 1 v 2 where h is the perpendicular distance from the point the light ray hits the mirror to the optical axis. Spherical aberration can be reduced by not using spherical mirrors. A parabolical mirror has no spherical aberration for light rays parallel with the optical axis and is therefore often used for telescopes. The used signs are: Quantity + - R Concave mirror Convex mirror f Concave mirror Convex mirror v Real object Virtual object b Real image
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Unformatted text preview: 6.2.3 Principal planes The nodal points N of a lens are de±ned by the ±gure on the right. If the lens is surrounded by the same medium on both sides, the nodal points are the same as the principal points H. The plane ⊥ the optical axis through the principal points is called the principal plane . If the lens is described by a matrix m ij than for the distances h 1 and h 2 to the boundary of the lens holds: h 1 = n m 11-1 m 12 , h 2 = n m 22-1 m 12 ± ± ± N 1 N 2 O 6.2.4 Magnifcation The linear magnifcation is de±ned by: N =-b v The angular magnifcation is de±ned by: N α =-α syst α none where α sys is the size of the retinal image with the optical system and α none the size of the retinal image without the system. Further holds: N · N α = 1 . For a telescope holds: N = f objective /f ocular . The F-number is de±ned by f/D objective ....
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