
Marginal and chief rays
Much of the analysis of a lens system can be done by tracing two rays: the marginal ray and the chief ray. These rays lie in the tangential plane. Because of the importance of these rays, it is essential that you be familiar with their definitions. Unless explicitly specified, the marginal and chief ray are paraxial rays, in the sense that they are traced through the system using paraxial formula.
The marginal ray is the ray that leaves the intersection of the object plane and the optical axis (z) at an angle that causes the ray to hit the edge of the aperture stop.
The chief ray is the ray that leaves the object plane at the maximum object height and at an angle that causes they ray to hit the center of the aperture stop.
Finite conjugate system
The marginal and chief rays are pictured below for a finite conjugate system (object at finite distance from the lens). The marginal ray is drawn red, the chief ray is drawn green. The lens is the shaded block, with an internal aperture stop. Inside the lens the rays follow paths that take the marginal ray to the edge of the aperture stop, and the chief ray to the center of the aperture stop.

Infinite conjugate system
If the object plane is at infinite distance, the marginal ray is parallel to the axis, and the chief ray has the maximum field angle. For tracing purposes, we start the rays at a reference plane (usually the plane containing the vertex of the first glass surface of the lens). At the reference plane the height of the marginal ray from the axis is the entrance pupil radius. For a lens being designed for a 20 degree field of view, the chief ray makes an angle of 20 degrees with respect to the optical axis. The marginal and chief rays are pictured below for this case.

Relation to reduced (normalized) coordinates
The marginal ray has reduced field coordinates Hx=0,Hy=0 and reduced pupil coordinates Px=0,Py=1.
The chief ray has reduced field coordinates Hx=0,Hy=1 and reduced pupil coordinates Px=0,Py=0.