# New PDF release: Gesammelte mathematische Werke 3

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X2o : x2i : 3. x3o : x3i : 4. x4o : x4i : mm1 −20. 25. −10 n2 + n1 x2o n2 + n1 x3o n2−n1 r x2i −30 mm2 : x3i 15 mm3 : x2i · n1 x2o · n2 2. 5. 7. 1. 1 for refractive indices n1 2. 167. 4 (Diamond). 4 and n2 1. 1 Geometrical Construction for Real Objects to the Left of the Object Focus We consider an extended object consisting of many points. A conjugate point at the image corresponds to each point. When using a spherical surface for image formation, a cone of light emerges from each object point and converges to the conjugate image point.

Rewriting Eq. 48) xo /n1 , ζi xi /n3 , ρ1 xi , we have (n2 − n1 )/r1 + (n3 − n2 )/r2 . 50) and depends on the refractive indices outside and inside the lens, and on the two radii of curvature. In most cases both sides of the lens have the same refractive index 1; that is, n3 n1 1. Calling the refractive index of the lens n, we have 1/f (n − 1)/r + (1 − n)/r . For a symmetric lens in air we obtain 1/f 2(n − 1)/r. Using n3 n1 1 and the focal length of Eqs. 50), we have from Eq. 49) the thin lens equation, −1/xo + 1/xi 1/f.

Change the refractive index and describe what happens. 3. Change the focal length and describe what happens. 28 1. 11 (G11TINPOS) Calculation of image and object foci for f 10. Calculation of image distances xi and magnification for four specific values of object distance xo G11TINPOS Positive Lens Focal length f is positive, light from left propagating from medium with index 1 to lens of refractive index n. xo on left of lens (negative). Calculation for Four Positions for Real and Virtual Objects, to the Left and Right of the Object Focus and Image Focus Calculation of xi from given xo and focal length.