Ray transfer martix of interface

[nanguaa]

I found two different descriptions about ray transfer martix of interface in two textbook. I am confused about this. which one is correct? I hope someone can help me.
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A:Lasers, A.E.Siegman,pp586
B:Laser Resonators and Beam Propagation, N.Hodgson, pp16

 

[Andy Resnick]

Siegman's is the one I am used to seeing- that is the refraction matrix written out using the paraxial approximation and the (y, nu) form for rays. I don't immediately see how to transform Siegman's into Hodgson's, but maybe Hodgson is using a different ray notation?

 

[nanguaa]

I check these two descriptions again, and I found that the difference may be caused by the understanding about optical path.

example:Plane Dielectric Slab