I'm having a hard time picturing how these are out of phase and in phase for the different set up . I thought for set up one would be in phase then out of phase. Since they are only a difference of one pi. This is hard for me to see . This is on page 285 of physics TBR .
The key here is recognizing that in set-up one, there is only one reflection-generated phase shift (air off glass) while in set-up two there are two different pathways each of which have one reflection-generated phase shift (air off glass for one and glass of plastic for the theory). But every pathway show that involves reflection has just one reflection-generated phase shift.
Are you referring to question #38? If you consider the two pathways in question, one never leaves air, reflecting off the glass for a 180˚ phase shift. The other goes from air to glass and the reflects off plastic (which has a higher index of refraction), which also causes a 180˚ phase shift. So both pathways have equal phase shifts. The question states that the two pathways are different by 180˚ in phase, so that different has to be attributed to a difference in their pathways. The light that travels into the glass and reflects off the plastic is traveling further. It's greater distance is equal to lambda/2, 3(lambda)/2, 5(lambda)/2, etc. Keep in mind that the distance is "there and back" through the thickness of the material. If the there and back distance is lambda/2, then the thickness of the glass must be lambda/4. The wavelength is 1.00 m, so the thickness of the glass must be one-fourth of that = 0.250 m.