Phase Difference of a light wave

AI Thread Summary
The effective phase difference of light waves with a wavelength of 540 nm and a path length difference of 3600 nm is calculated using the formula φ = (2π/λ) * ΔL. The initial calculation yields a phase difference of 41.88 radians, which is significant but needs to be interpreted in terms of cycles. Since phase is cyclical, the relevant phase difference is determined by the excess beyond full cycles, leading to a final answer of 120°. Understanding that phase differences can wrap around is crucial for accurate interpretation. The discussion emphasizes the importance of considering the cyclical nature of phase in wave mechanics.
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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