## C1 Derivation

Figure C-1 displays an "unfolded" Newtonian and defines various quantities useful in this derivation. These variables are f, the focal length; D, the diameter of the mirror; s, the sagitta (or depth) of the mirror; T, the distance from the focal plane to the center of the tube; and L, the diameter of the fully-illuminated region at the focal plane. In this derivation, I will determine the values of the minor (short) axis of the diagonal and the sideways or down offset of its center. The coordinate system is defined with its origin at the center of the focal plane. The x-axis extends through the center of the mirror, and the y-axis extends laterally away from the optical axis.

Fig. C-l. The coordinate system and quantities of interest in .sizing and properly placing the Newtonian diagonal.

Fig. C-l. The coordinate system and quantities of interest in .sizing and properly placing the Newtonian diagonal.

Three lines of Fig. C-1 are significant. Lines #1 and #3 follow the edges of the fully-illuminated field to the edges of the mirror. Line #2 is directed along the surface of the diagonal. We know it is at 45° and therefore strikes the two axes at the indicated points having coordinates (0,7) and (T,0). Similarly, we know the coordinates of two points along each of the lines #1 and #3, and we can use this knowledge to obtain the defining equation of those lines as well.

Once the equations of the lines are known, the points of intersection at the far edges of the diagonal can be calculated. These intersections have coordinates (xa,ya) and (xb,yb). These points are all that are required to derive both the minor axis and the offset. The minor axis is

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