Reading assignment: 37.4-37.6,37.7 (if your edition of the textbook has it)
In Fig. 37.9 (8th edition) the textbook compares the reflection of light from
a surface to the reflection of a wave on a rope. How does the analogy work?
When an upward pulse on a rope hits a rigid support, it flips to be a downward pulse. That's a 180 deg phase change. When an upward pulse hits a free support, it reflects back still upward. That's a 0 deg phase change. The analogy is that light hitting a higher index material is like rope wave hitting rigid support, and light hitting a lower index material is like rope wave hitting free support. CAUTION! this analogy only works for close to normal incidence, i.e. 0 deg. (this fact not mentioned in book).
The concept of "optical path length" (OPL) is used in many places to analyze
optical problems. (Unfortunately your textbook doesn't use it.) See for example
http://en.wikipedia.org/wiki/Optical_path_length. In materials with a
constant index of refraction n, the OPL is just the path length times
n. In the context of today's reading, why might that be a helpful
The path length, times n, is precisely the left hand side of equations 37.17 and 37.18 (8th edition). Viewed that way, those equations are identical to the constructive/destructive interference conditions we learned for sound, back in Chapter 18.