- #1
DrBanana
- 47
- 3
- TL;DR Summary
- I want to understand why rotating the interferometer results in a fringe shift at all
Ok for the interferometer let the arm lengths be ##L##, speed of light relative to the aether be ##c## and the speed
of the setup relative to the aether be ##v##. By calculation you can show that the distance between the two 'heads'
of the beams of light is ##\frac{v^2L}{c^2}##, and using the convention of the Wikipedia article, we denote this difference as a difference of wavelengths, so ##\Delta \lambda = \frac{v^2L}{c^2}##.Now rotating the setup by ninety degrees, it's intuitive that the absolute value of the difference doesn't change. But what I don't understand is why this time we take ##\Delta \lambda _2=-\frac{v^2L}{c^2}##. That is, why does the 'order' of the lengths matter here? Both beams have the same wavelength and the same frequency, so the interference pattern should be the same, so why is that not the case?Also I'd like to know how to calculate fringe shifts (given path differences) in the first place. In my textbook's optics chapter there's only talk of Young's double slit experiment, which is for two light sources that are separated by some distance, which is not the case here.
of the setup relative to the aether be ##v##. By calculation you can show that the distance between the two 'heads'
of the beams of light is ##\frac{v^2L}{c^2}##, and using the convention of the Wikipedia article, we denote this difference as a difference of wavelengths, so ##\Delta \lambda = \frac{v^2L}{c^2}##.Now rotating the setup by ninety degrees, it's intuitive that the absolute value of the difference doesn't change. But what I don't understand is why this time we take ##\Delta \lambda _2=-\frac{v^2L}{c^2}##. That is, why does the 'order' of the lengths matter here? Both beams have the same wavelength and the same frequency, so the interference pattern should be the same, so why is that not the case?Also I'd like to know how to calculate fringe shifts (given path differences) in the first place. In my textbook's optics chapter there's only talk of Young's double slit experiment, which is for two light sources that are separated by some distance, which is not the case here.