Exploring Co-Phasal Wave Fronts in Fizeau Interferometry

[Ahmed123]

TL;DR Summary

Question and discussion about wave fronts and phases of the rays at the Fizeau interferometer

I am studying Fizeau analysis for wedge problem. I reached to this part and I cant follow. I have two questions and any help will be appreciated
1) what is meant by co-phasal wave fronts? does it mean that they have the same phase? ( how can I Think about the wave fronts in this case)
2) why the pass difference between the two rays is calculated by this formula?

Thanks in advance

 

[sophiecentaur]

TL;DR Summary: Question and discussion about wave fronts and phases of the rays at the Fizeau interferometer

what is meant by co-phasal wave fronts?

It means that the waves emerging along both paths are in phase. That will happen when the lengths of the two paths differ by a whole number of wavelengths. So the distance travelled in the diagram between the blue exit point and the red exit point will be one, two three . . . . whole wavelengths. The term is "Path Difference" and not 'pass difference' (translation problem, no doubt).

An easier example to start with is when the plates are parallel and the incident wave is plane; you get full addition, all over the emerging wave for one angle (say normal) and cancellation at another angle. Put the appropriate angles in your calculations and it should work for that.

PS it's always worth while looking at more than just one source to resolve this sort of confusion. There are dozens available.

 

[gravisxv]

The wavefronts are planes perpendicular to the direction of propagation. This means that the wavefronts are in phase with each other, and they will interfere constructively.

 

[sophiecentaur]

The wavefronts are planes perpendicular to the direction of propagation. This means that the wavefronts are in phase with each other, and they will interfere constructively.

Where? It is angle dependent.

 

[sophiecentaur]

I'm not sure where they get the final equation without a bit more help. Is there any more text that you could copy here?
Is there a link to the whole text?

 

[sophiecentaur]

@gravisxv We may be talking at cross purposes. It isn't clear if you actually understand how interference is caused when two path lengths are involved. How familiar are you with the basic way in which the fringes are generated by the two slit experiment?

 

[gravisxv]

It is certainly angle dependent. I understand what you're telling, in the Fizeau wedge interferometer, the path difference between the rays depends on the angle at which they emerge from the wedge.

 

[sophiecentaur]

It is certainly angle dependent. I understand what you're telling, in the Fizeau wedge interferometer, the path difference between the rays depends on the angle at which they emerge from the wedge.

If you accept that, then how would you not get fringes?
The details of that equation under your quoted diagram would need some fleshing out. I asked you for more info or a link. Do you have it?

Alternatively, look for another source and we could discuss that. You can't expect a one stop shop on Google.