How can it be explained using the laws of refraction that a light through optical centre of a lens passes undeviated?
If we assume the portion of the lens in the middle to be made of even number of alternately place up and down prisms, then it's clear, but why can the number of prisms not be odd?
Answer
Look at the lens as a slab of finite thickness. In a small vicinity around its center we may consider its opposing surfaces as parallel to each other. A ray incident on this area, at any angle, will be refracted twice at parallel interfaces. Therefore it will emerge on the other side of the lens on a direction slightly displaced, but parallel to the incident one. Since the parallel displacement is tiny as long as the lens is not too thick, it looks like the ray passes through the center undeviated.
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