Phase Difference of a light wave

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Homework Help Overview

The problem involves calculating the effective phase difference of light waves when two beams, originating from the same source and having a wavelength of 540 nm, travel along different paths with a path length difference of 3600 nm.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of phase difference using the formula provided, with one participant expressing confusion over the results obtained. There is a focus on understanding the cyclical nature of phase and how to interpret large phase values.

Discussion Status

Some participants have provided calculations and interpretations regarding the phase difference, noting the importance of considering the cyclical nature of phase shifts. There is an ongoing exploration of how to express the phase difference in terms of cycles.

Contextual Notes

Participants are working with specific values for wavelength and path length difference, and there is mention of potential unit errors that may affect the calculations. The discussion reflects a need to clarify assumptions about phase relationships.

Erubus
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Homework Statement


Light with wavelength 540 nm is split into two beams that travel along two paths. The difference between the path lengths is 3600 nm. What is the effective phase difference when the light recombines?


Homework Equations


\phi = (2pi/λ)*ΔL


The Attempt at a Solution


It seems like a simple problem, I plug in 540 for λ and 3600 for ΔL but I'm not getting the right answer.
 
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Show us your calculations. What answer are you getting?
 
\phi = (2pi/(540x10^-9) * 3600x10^-9 = 41.88

answer is 120°
 
Erubus said:
\phi = (2pi/(540x10^-9) * 3600x10^-9 = 41.88

answer is 120°

Sure, the phase difference is 41.88, which is a huge number, but remember that phase is cyclical. If the phase difference were 4pi, would this be any different from the case where the phase difference were 2pi, or 0? No, because all of these correspond to a shift by a whole number of cycles. A full cycle causes you to increase in phase by 2pi RADIANS.

Note: the word in all caps above also hints at a second error you were making, involving units. So, the question you have to answer is, how far out of phase are they two waves actually, given that 41.88 radians corresponds to a whole number of cycles + some excess? It's this excess (which is less than a full integer of cycles) that you're interested in, because it tells you how out of phase the waves are.
 
Got it, thanks.
 

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