AP 2 mirror problem

Here is my take on the two mirror problem Ch23 #1. The book seems to think that one only needs to consider how far the second mirror is behind you (ten feet) and you add this 10 ft distance to the initial 10 feet between person and his first reflection once for each additional reflection. 

I don't know where this reasoning comes from since the source of the image in mirror 2 is a reflection from mirror 1 . My approach is to construct the straight path of the ray of light that hits the eye back to where it originates including all the reflections.  See if you accept my reasoning or tell if I missed something.

http://h1.ripway.com/DrCherdack/2Flatmirrapprnt%20dist.doc