## Offset xcenter T XaXb TC

Lines have the general form y = mx + b, where b is the y-intercept and m is the slope. Line #2 is the easiest to determine, and by inspection one

C.1. Derivation

Line #1 has a y-intercept of L/2, and the slope can be obtained by inserting the known coordinates of the point at the upper corner of the mirror:

Thus,

2( f - s) 1 2 Similarly, the equation of line #3 becomes

We can rename the quantity (D â L)/2fâ s) = n. All three equations can be summarized as y1 = nx1 + y,y2 = -x2 + T,y3 = -nx3 -L (C.6)

By setting y1 = y2, we can determine the coordinate xa as

1 + n and we insert that expression back into the line #2 equation to derive ya:

Similarly, the coordinates of the other intersection point are x, = ^ and y =- + T. (C.9)

The expression for the minor axis (Eq. C.1) is just the difference between the two y-values:

The offset (Eq. C.2) is only a little more complicated:

Offset = 1 f T - (L/2) + T +(L/2) 1-T or Offset = - T. (C.11)

The final expressions of Eqs. C.10 and C.11 are exact. They only require an expression for the sagitta. A parabola of focus f is determined by the equation x = f - (y2/4f), and the exact sagitta is obtained by evaluating the shift in x on axis and at the y-value of the edge, D/2:

Please note that Eq. C.12 is not the same as the wavefront sagitta that will be calculated in Appendix E, but the surface sagitta, which is half as large.

Was this article helpful?

Through this ebook, you are going to learn what you will need to know all about the telescopes that can provide a fun and rewarding hobby for you and your family!

Get My Free Ebook

## Post a comment