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Combination of Lenses

When we view an object through several lenses which are near each other, then it is possible to treat the combination of lenses as one lens.
Combination of Lenses
When several lenses with focal lengths f1, f2,…. arc near each other, then the combination has a focal length ftotal given by


The quantity 1/f for a lens is called the power of the lens, measure in [m–1 = diopters = D]. This word power has nothing to do with the other definition of power, that is, energy per time. The point here is that the power of a combination of lenses is the sum of the power of the lenses.

Dieter has an eye which, when the eye is at rest, focuses light to a point 0.024 m behind the lens, which is 0.001 m in front of the retina. What is the power of the corrective lens he must wear?



The power of Dieter's eye is Peye = 1/0.024m = 41.67 D. The combination of lenses should have a focal length 0.024 m + 0.001 m = 0.025 m, so the power of the combination of the two lenses needs to be Pcombo = 1/0.025 m = 40 D. Since Pcombo = Peye + Pcorrect, we have Pcorrect = –1.67 D.

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