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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?

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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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    $\begingroup$ Note that ignoring the parallel displacement is essentially what we mean by the paraxial approximation. $\endgroup$
    – John Rennie
    Commented Oct 27, 2015 at 11:59
  • $\begingroup$ Also, you can think of the lens as multiple stacked prisms which are obviously inverted around the centre. I like this idea better because it's addressed in so many text books and can be seen in the recombination of light as well! $\endgroup$
    – user220704
    Commented Apr 3, 2020 at 13:59
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Truth is that the light does not pass through undeviated,we just assume it passes through undeviated, this is because we make the thin lens assumption.we assume that the lens we are dealing with is thin and in such lenses,when light is directed towards the optic centre the light ray refracts once while entering the lens and the second time while exiting the lens but since the lens is thin the light wouldn't have travelled a large distance in the lens therefore when the light exits the lens the amount of deviation from the path light would have taken if there were no lens would be very less( very negligible ) ............butto keep things simple we say just say that the light ray passes through undeviated.

But keep in mind , as the lens gets thicker and thicker the deviation will become larger. ;)

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The middle part of the lens will just act as a rectangular glass slab. We may verify it by cutting the lens horizontally. Now we know that rectangular glass slab refract light in such a way that emergent is parallel to incident. Actually the same happens when the ray passes through optical centre. This can be observed in a thick lens. In thin lenses the perpendicular distance between extended incident ray and extended emergent ray is negligible. So we can say that light ray passes through optical centre without deviation.

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  • $\begingroup$ How is that any different from what the first answer means? $\endgroup$
    – Quark
    Commented Feb 2, 2016 at 19:23
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Actually the same happens when a ray of light passes through optical centre the perpendicular distance between extended incident ray and extended emergent ray is negligible so...we can say that the ray which passes through the optical centre is undeviate.

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