Principal Axis
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Is the straight line joining the centers of curvatures of the two curved surfaces of a lens.
Principal Foci
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Rays of light can pass through the lens in any direction and hence there will be two principal foci on either side of the lens and they are referred to as the first principal focus and the second principal focus of a lens.
First Principal Focus (F1)
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It is a point on the principal axis of the lens such that the rays of light starting from it (convex lens) or appearing to meet at the point (concave lens) after refraction from the two surfaces of the lens become parallel to the principal axis of the lens.

First Principal Focus of a Convex Lens

First Principal Focus of a Concave Lens
The distance from the optic center to the first focus is called the first focal length (f
1) of the lens.
Second Principal Focus (F2)
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It is a point on the principal axis of the lens such that the rays of light parallel to the principal axis of the lens after refraction from both the surfaces of the lens pass through this point (convex lens) or appear to be coming from this point.

Second Principal Focus of a convex lens

Second Principal Focus of a concave lens
The distance from the optic center to the second principal focus is called the second focal length (f
2) of the lens.
If the medium on both sides of the lens is same then the first and the second focal lengths will be equal.
Focus of a convex lens is real whereas that of the concave lens is virtual.