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I want to clear my mind on one basic optics thing:

If I have a point source some distance away from a lens, the position of the image formed can be found using traditional geometrical optics ray approach: one ray passing through the center of the lens and another one parallely to the axis and through the focal point.

If I think about this situation as if the rays are the plane waves: I decompose the light coming from the point source into infinitely many plane waves each reaching the lens at some angle. Now I can draw infinitely many rays for each plane wave which are perpendicular to the plane waves front and all these rays are going through the lens. And I get a lot of different ray directions after the lens, no image is formed. So is there the one exact path during which a ray must be drawn if a plain wave is infinite?

Thank you for clearing this up for me.

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Rays in geometrical optics are regarded as "pencils" of light: vanishingly narrow "tubes". This, of course, is not physically possible in the wave picture of light. Thus, it is an idealization.

Rays are also used to describe the wave vector of a plane wave. Of course, this is a wave property, and also an idealization. The ray can be drawn anywhere in space as long as it is normal to the phase front. All of this you clearly understand.

The issue is simple: there are two meanings of the word "ray", and which one applies depends on the context. Born and Wolf (standard tome on optics) is careful to use the word "pencil" rather than "ray" in the geometrical optics context.

When doing ray tracing, you should keep the first definition in mind and pretty much forget about the second definition.

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