I was thinking about the basic structure of interferometers and I watched a video about it. I came across a simple illustration that looked something like this:
A laser beam is split into two seperate beams with half intensity by a beam splitter, each with probability 1/2. The reflected beam should have a phase change of +π. The transmitted beam should have no phase change. Both beams hit a mirror at 90 degrees, and both get shifted by +π again, and hit another beam splitter. My question is: Why does the whole recombined beam hit the detector?
To my understanding, beam A) should hit the second splitter and be transmitted (so it stays at phase change +2π) and be reflected (resulting in phase change +3π), and beam B) should be transmited (stay at phase change +π) and be reflected (resulting in phase change +2π). So there should be two resulting beams; there should be no destructive interference.
Where is my reasoning wrong and why is there destructive interference athe the second beam splitter resulting in the detector registering the whole original beam?
Thanks in advance