Interference patterns and fringe shift in interferometers

Not sure if this is entirely the right place to ask about this. I've been reading about special relativity, I understand the Fitzeau and Michleson Morely experiments, i.e the goals of them and why the apparatus is set how it is, and I can follow most of the maths. The part I don't get, and my main question here, is although I totally get that spinning the Michleson Morely interferometer would cause a change in the interference pattern (if there were an ether) due to path difference, and that the interference pattern from the fitzeau experiment will depend on the path difference between the rays of light passing through the water either way, I don't get as to how the path difference is calculated from the fringes. The book talks about fringe shifts, and it really does not make it clear as to what has been measured for the Fitzeau experiment. I have possibly slightly limited knowledge of optics, I am actually a second year mathematics student, although I did well at A level maths, and I'm just reading this for interest. If I need to study optics further in order to understand this quantitatively, I would appreciate it if anyone could recommend me a book that would explain it to me, or any other relevant resource.

Thanks.

Reply 1

Joinedup

20

Original post by Associativity

Not sure if this is entirely the right place to ask about this. I've been reading about special relativity, I understand the Fitzeau and Michleson Morely experiments, i.e the goals of them and why the apparatus is set how it is, and I can follow most of the maths. The part I don't get, and my main question here, is although I totally get that spinning the Michleson Morely interferometer would cause a change in the interference pattern (if there were an ether) due to path difference, and that the interference pattern from the fitzeau experiment will depend on the path difference between the rays of light passing through the water either way, I don't get as to how the path difference is calculated from the fringes. The book talks about fringe shifts, and it really does not make it clear as to what has been measured for the Fitzeau experiment. I have possibly slightly limited knowledge of optics, I am actually a second year mathematics student, although I did well at A level maths, and I'm just reading this for interest. If I need to study optics further in order to understand this quantitatively, I would appreciate it if anyone could recommend me a book that would explain it to me, or any other relevant resource.

Thanks.

I found a video of a repeat of the experiment - I think it's a copy of the improved setup used by Michlson to do the Fizeau experiment rather than the classic Fizeau.

at the end you can see the fringe pattern move (but not much) when he switches off the water - the displacement of the fringe pattern is plotted against the velocity of the water and you can see that the observations don't agree with classical theory.

hope that's what you need to visualise it.

Reply 2

james153

1

If I recall correctly, you view circular fringes at the viewing position, basically lots of concentric circles.

Slowly increasing the path difference, such as moving one of the
mirrors, causes new fringes to appear at the centre, and ones at the outside to fade out of sight. Each white fringe coincides with a region of constructive interference between the two beams, which corresponds to an increase in the path difference of 1/2 the wavelength of light being used.

When viewing the interference pattern directly, the relationship between the numbers of new fringes appearing/number of old ones disappearing is equal to twice the path difference over the wavelength:

2d=n*lambda

(sorry haven't figured out how to put equations in).

I appreciate this isn't a rigorous derivation of the equation, but I hope it helps a bit.

Reply 3

Associativity

OP

9

Thanks for that Joinedup.

That was a really great video, I really liked seeing the pattern move like that, and I really enjoyed it. However, my question was more along the lines of, why does a change in path difference cause the fringes to shift. I understand that the interference pattern would change, but what I don't understand is why it appears to shift, and how you can correlate fringe shifts with changes in path difference.

Reply 4

0le

21

You'll probably have to read a little about Mie Scattering theory to understand that. (educated guess).

Regarding the path difference, Koenig linked path difference to particle diamater. When light is scattered from a particle in the foreard scatter regions (30-80 degrees), then you can reduce Mie scattering theory to geometric optics, provided the size parameter (the size of the particle) is large enough. When using geometric optics in this scatter region, the fringe pattern observed is due to the phase difference between the "first order refracted" and reflected ray.The other fringe patterns collected by a lens (say your doing some PIV experiment or something but on large particles) would be "shifted" presumably because you're looking at a different scattering angle and thus the leaving rays (the first order refracted and reflected ray) are now different.

I'm not entirely sure that is what you meant but maybe that can guide you into some work that might fully answer your question.

EDIT: Yeah, nevermind, discard all of that.

(edited 9 years ago)

Reply 5

Joinedup

20