Young's double slit and coherent light

[sorax123]

Hello all,
I was looking through my textbook on the double slit and it talks about constructive interference occurring at path differences of m $\lambda$ and destructive interference occurring at path differences of (m + 1/2) $\lambda$ where m is an integer. This is obvious if the waves leave the 2 slits in phase, however the book states that it is not necessary for the waves to be in phase, just for them to be coherent (ie. constant phase difference). Now I understand how the fringe pattern would form here but I fail to understand how the above conditions can be true as for the two to be in phase, one would have to travel further to be in phase at the arbitrary point P. Is this a textbook oversight or am I missing something?
Thanks,
Dom

 

[mfb]

If the incoming light has different phases at the slits, the points of constructive/destructive interference will be different as well, right.

 

[sorax123]

So the constructive interference only occurs at m $\lambda$ if in phase at the slits as I assumed?

 

[mfb]

Right.

 

[sorax123]

I see, thanks very much for clearing that up.