Answer in just 1-4sentences.how do you conclude that a ray of light incident towards the optical centre of a thin lens is transmitted without any deviation
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 )
To 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.