Page:BatemanConformal.djvu/19

From Wikisource
Jump to navigation Jump to search
This page has been validated.
88
[Nov. 12,
Mr. H. Bateman

The linear magnification in the new system is

Let c be the distance of the second interface from the first; then we associate the length -c with the second interface B, and the formulæ of the transformation become

The last of which may be written

i.e.,

where z and x' are measured, as before, from the first surface. This is exactly the former relation between two corresponding points; consequently the whole course of a ray in one instrument corresponds in the transformation to that of the corresponding ray in the corresponding instrument.[1]


  1. We can verify the equation

    connecting two conjugate points in the second instrument as follows

    and

    since Q" and Q' are conjugate points in the first instrument; hence the relation is satisfied.