Observing wavelength at an angle

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    Angle Wavelength
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Discussion Overview

The discussion revolves around the observation of wavelength at an angle relative to the direction of wave propagation, particularly focusing on the implications of the equation ## \lambda_{ob} = \frac{\lambda}{cos(\alpha)} ##. Participants explore the meaning of observing wavelengths at different angles and the concept of phase differences in relation to wavefronts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the meaning of observing wavelength at an angle and questions how standing perpendicular to the wavefront could lead to an infinite wavelength perception.
  • Another participant clarifies that while the observed wavelength does not change, the phase difference between points on the observation plane remains constant, suggesting that the equation describes the spacing of maxima rather than a true wavelength.
  • A participant seeks further clarification on the concept of maxima appearing infinitely far apart when viewed perpendicularly to the wave's direction.
  • It is noted that the distance along the observation plane appears "infinite" because the same maximum is observed simultaneously, while the actual wavelength in the direction of travel remains unchanged.
  • A participant reflects that visualizing the wave as stationary while moving against the wavefront at an angle helped their understanding.

Areas of Agreement / Disagreement

Participants express differing views on the utility of referring to the observed distance between maxima as "wavelength." There is no consensus on the interpretation of the implications of observing wavelengths at an angle.

Contextual Notes

Participants discuss the relationship between the observed wavelength and the phase differences, indicating that assumptions about the definitions of wavelength and observation planes may affect interpretations.

TheCanadian
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I recently came across an equation stating that ## \lambda_{ob} = \frac{\lambda}{cos(\alpha)} ## if ##\alpha## is the angle the observer is relative to the wave's direction of propagation. I guess I can kind of understand that a person perpendicular (i.e. ##\alpha = 1##) would see the normal wavelength, but am just failing to understand what exactly it even means to observe the wavelength at an angle. How does standing perpendicular to the wavefront make it look like the wave has an infinite wavelength?
 
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It does not, but if you look at the phase difference between different points of your "observation plane", they all have the same phase. This equation tells you how far apart maxima (or specific phases) are on your observation plane. I don't think it is useful to call this "wavelength", however.
 
mfb said:
It does not, but if you look at the phase difference between different points of your "observation plane", they all have the same phase. This equation tells you how far apart maxima (or specific phases) are on your observation plane. I don't think it is useful to call this "wavelength", however.

Hmmm...do you mind expanding on that? How exactly does the maxima look infinitely far away from each other if you're simply looking at the wave perpendicular to its direction of propagation?

Also, isn't the distance separating maxima essentially what an observed wavelength is?
 
The distance along the observation plane is "infinite" (you see the same maximum everywhere at the same time). The distance along the travel direction (the real wavelength) does not change.
 
mfb said:
The distance along the observation plane is "infinite" (you see the same maximum everywhere at the same time). The distance along the travel direction (the real wavelength) does not change.

Thinking of the wave as stationary and myself moving against the wavefront at the angle ##\alpha## really helped! Thank you!
 

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