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For a given bundle of rays entering the lens from a given point a wide aperture produces a cone of rays that hit the focal plane as a tiny focused point known as the circle of confusion (I.e. the smallest resolvable dot). If you move the focal plane forward or backward a tiny amount the circle of confusion becomes quite large, (I.e. starts to produce a blurry image) this is because the focal plane intersects this cone of rays at a different place now. The wide aperture produces a wide angle cone of rays (or think of it as a dumpy cone), so a small shift in focal plane makes a large difference in the size of the circle produced by intersecting the cone of rays with the focal plane (because the effective apex angle of the cone is large). If on the other hand you stop down to a small aperture the cone of rays becomes much narrower (I.e. a pointy cone rather than a dumpy cone). If you then shift your focal plane forward or back by the same amounts as before you will find that the circle of confusion is much smaller (I.e. the size of the circle produced by intersecting the cone with a flat plane is smaller because the apex angle of the cone is much smaller or narrower). These focal plane shifts translate into equivalent depths of field. Narrow bundles of rays from a small aperture produce greater depths of field as the circle of confusion remains small.
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