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A compound light microscope has two lenses: the objective lens (the lens closest to the specimen) and the eyepiece lens (the lens through which an image is viewed).

My textbook states that chromatic aberration is reduced through the use of a double lens, rather than a single lens. How is this so? Does it work like an achromatic doublet, in which the chromatic aberration is cancelled by using a convex and concave lens together?

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In a word: yes, but you may be missing the point of an achromatic doublet. An achromatic doublet works by combining two lenses made of different materials, whose dispersion relations cancel each other out. So any compound lens system where all the lenses are made of the same material does not reduce chromatic aberration.

What I think the book was trying to do was point out that there were ways to reduce chromatic aberration without going into the specific way in which this was done.

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