Can the tilt of the mirrors affect the arm length and travel time in the Michelson experiment ?

Does changing the angle of the mirrors in the Michelson-Morley experiment affect the arm lengths and travel times ? Since the mirrors were tilted from the edge and not from the center, a small difference in path length surely must occur ? If the mirror is tilted toward the beam splitter, then the path length will be shorter aka contract, and if it is tilted away from the beam splitter, it will be bigger.


GEMINI: 

You are completely correct about that physical detail: if a mirror pivots from its edge, the center of the mirror physically moves closer to or farther from the beam splitter.

Here is exactly how that mechanical shift impacts the experiment:
1. The Physical Arm Length Does Change
Because the pivot point is at the edge rather than the exact center, tilting the mirror introduces a small mechanical displacement (
) at the point where the laser beam hits.
  • Tilt Towards Splitter: The physical distance decreases.
  • Tilt Away from Splitter: The physical distance increases.
2. The Impact on Travel Time
This change in distance directly alters the light's travel time (
t
). Because the beam must travel to the mirror and back, the round-trip travel time changes by:
Δt=2⋅ΔLc

(where 
c
 is the speed of light)
3. What You See in the Experiment
In a real laboratory setting, this edge-pivot effect causes two things to happen simultaneously when you turn the alignment screw:
  • Fringe Separation (Due to the Tilt): The interference rings transform into straight, parallel lines because the two combining wavefronts are no longer perfectly parallel.
  • Fringe Shifting (Due to the Distance Change): The lines will rapidly march across the screen. Each time the center of the mirror moves by just half a wavelength of light (
    ), one full fringe will pass by.
Because light wavelengths are so tiny (hundreds of nanometers), even a microscopic edge-tilt creates a massive, easily visible shift in the fringe pattern.
Are you currently trying to align an interferometer in a lab, or are you calculating the mathematical error introduced by this edge-pivot mechanic?
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