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At page 135 of Max Born's "Principles of Optics", he proves the statement that there are two foci on each ray of a rectilinear congruence.
Here a rectilinear congruence of light rays is defined as a collection of straight light rays such that for each point in space there is one ray of the congruence going through that point.
A foci is defined as a point on a specific ray such that the distance to a neighbouring ray vanish to first order.
Question: Intuitively, I would think that straight rays would just converge at a single point, not two. How can it be two places on a single straight ray where it get "close" to its straight neighbouring rays?
Here a rectilinear congruence of light rays is defined as a collection of straight light rays such that for each point in space there is one ray of the congruence going through that point.
A foci is defined as a point on a specific ray such that the distance to a neighbouring ray vanish to first order.
Question: Intuitively, I would think that straight rays would just converge at a single point, not two. How can it be two places on a single straight ray where it get "close" to its straight neighbouring rays?