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Lens Paradox
Usually in the elementary textbooks of physics the focusing action of a lens is explained by referring to a prism. The normal ray in the middle passes without bending and the lower ray bends because of the refraction of light as in a prism. Consider an alternative construction of the lens as composed of circular discs of varying radii stacked together (this is how the volume integral of the lens would be evaluated). In this construction the normal rays pass without bending at all. In the alternative construction there is no focusing. A paradox !