Two converging lenses having focal lengths of f1 = 10.7 cm and f2 = 20.0 cm are

Question

Two converging lenses having focal lengths of f1 = 10.7 cm and f2 = 20.0 cm are placed d = 50.0 cm apart, as shown in the figure below. The final image is to be located between the lenses, at the position x = 27.9 cm indicated. http://www.webassign.net/sercp9/23-p-044.gif (a) How far to the left of the first lens should the object be positioned? cm (b) What is the overall magnification of the system? (c) Is the final image upright or inverted? upright inverted

Explanation / Answer

a)if the final image is 27.9 cm to the right of f1, it is 22.1 cm to the left of f2; we use the thin lens equation to find the object distance for the final image: 1/o + 1/i = 1/f i=-22.1 cm since the image is to the left of the lens, so 1/o = 1/20+1/22.1 => o = 10.5 cm to the left of f2 or 50-10.49 to the right of f1 the object for f2 is the image for f1, so we now find o for f1: 1/o + 1/i = 1/f 1/o + 1/39.5 = 1/10.7 o = 14.7 cm to the left of f1 b)Magnification = v1v2/(u1u2) =-5.65 c)the image is inverted

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