What is the relationship between phase and path difference in waves?

[kira506]

What is meant by phase of a wave? I can't get a grasp of it especially after knowing that in an em wave ,the magnetic and electric fields E and B respectively are in phase , aren't they time varying and perpendicular to each other? Doesn't changing the inclination affect the phase ? Also,the phase difference ,I can't get it(this may sound stupid) when phase difference=0,does that mean that,say the 2 waves I'm measuring their phase diff. Are in phase ? And what are the possible equations by which I can determine the path difference between 2 waves? Thanks in avance !

 

[UltrafastPED]

For optics the electric field is usually chosen for simplicity; unless the light is in a waveguide there is a fixed relationship between the electric and magnetic fields.

Thus polarization is wrt the electric field; so is phase.

If two waves are in phase (phase difference is zero) then they constructively interfere; if they are out of phase by pi radians (180 degrees) they interfere destructively. And all other cases are intermediate.

In optics the phase difference can be calculated with the "optical path length", or OPL. So if you have two paths you calculate the OPL for each one, and their difference is the OPD="optical path difference". From the OPD you can determine the expected phase shift.

The OPL is the geometric distance x index of refraction; if these are varying along the way you chop up the path and apply the corresponding index of refraction.

They march through all of the theory and calculations for the Michelson interferometer here:
http://www.physics.umanitoba.ca/undergraduate/phys2260/Lectures/Intro%20Optics%20-%20PPT%20v2part%2004.pdfAlso see http://en.wikipedia.org/wiki/Optical_path_length

 

[Thomas_Phy_Eng]

Phase of a standard wave y= A*sin(wt+phi), where the same could be re written as y = A*sin(x). Now, as you know w- stands for angular frequency and t- time period , basically you find the entire term in the bracket speaks of angular displacement in physical sense, phi is the quamtity that distinguishes one wave from the other interms of time lag, when you say a wave y1 = A1*sin(w1t+phi) and another wave y2= A1*sin(w1t+phi+pi/2) , what we mean here is the second wave starts at a distance of pi/2 radians after the first wave this is just a physical sense of the entire wave concept. It speaks quantitavely of the lag between waves if there is one. It gives a complete picture because em waves have wide spectrum of different waves building it. In every day application you have low frequency waves, high frequency waves etc starting at different points in space time and buidling either constructively or destructively over the period of time. Therefore the only mathematical wave we can quantify the final wave and its amplitude is by acurately describing all parametrs like the amplitude of each wave, its angular frequency , time period and phase diff between the waves. I hope this answers your question. In EM waves both electric and magnetic fields are time varying which is true but they are in phas emeaning they occur at the same point in space time, on doesn't occur after the other they occur simultaneously.

 

[kira506]

For optics the electric field is usually chosen for simplicity; unless the light is in a waveguide there is a fixed relationship between the electric and magnetic fields.

Thus polarization is wrt the electric field; so is phase.

If two waves are in phase (phase difference is zero) then they constructively interfere; if they are out of phase by pi radians (180 degrees) they interfere destructively. And all other cases are intermediate.

In optics the phase difference can be calculated with the "optical path length", or OPL. So if you have two paths you calculate the OPL for each one, and their difference is the OPD="optical path difference". From the OPD you can determine the expected phase shift.

The OPL is the geometric distance x index of refraction; if these are varying along the way you chop up the path and apply the corresponding index of refraction.

They march through all of the theory and calculations for the Michelson interferometer here:
http://www.physics.umanitoba.ca/undergraduate/phys2260/Lectures/Intro%20Optics%20-%20PPT%20v2part%2004.pdf


Also see http://en.wikipedia.org/wiki/Optical_path_length

Thanks a lot , that really halped especially that I'm familiar with these terms , now I get the OPD and its relation to the phase of the wave

 

[kira506]

Phase of a standard wave y= A*sin(wt+phi), where the same could be re written as y = A*sin(x). Now, as you know w- stands for angular frequency and t- time period , basically you find the entire term in the bracket speaks of angular displacement in physical sense, phi is the quamtity that distinguishes one wave from the other interms of time lag, when you say a wave y1 = A1*sin(w1t+phi) and another wave y2= A1*sin(w1t+phi+pi/2) , what we mean here is the second wave starts at a distance of pi/2 radians after the first wave this is just a physical sense of the entire wave concept. It speaks quantitavely of the lag between waves if there is one. It gives a complete picture because em waves have wide spectrum of different waves building it. In every day application you have low frequency waves, high frequency waves etc starting at different points in space time and buidling either constructively or destructively over the period of time. Therefore the only mathematical wave we can quantify the final wave and its amplitude is by acurately describing all parametrs like the amplitude of each wave, its angular frequency , time period and phase diff between the waves. I hope this answers your question. In EM waves both electric and magnetic fields are time varying which is true but they are in phas emeaning they occur at the same point in space time, on doesn't occur after the other they occur simultaneously.

So they occur simultaneously but the periodic time differs ? So by saying that they occur simultaneously , you mean that do occur at the same time and space but this may change along their path and they'd be still in phase ? (Sorry for the trouble , i understand stuff slowly and thanks btw for the aforementioned information )