If n is infinity, wavelength is equal to what?

In summary, when n is infinity, the frequency of a wave increases, causing the wavelength to become infinitely small or zero. This is because infinity is a concept that represents something without limit, and as n approaches infinity, the wavelength becomes smaller and smaller without ever reaching a definite value. There is a formula for calculating the wavelength when n is infinity, which is λ = c / f, where λ is the wavelength, c is the speed of light, and f is the frequency. However, the concept of zero wavelength is only theoretical and cannot be achieved in reality. Both the concept of infinity in waves and in mathematics represent something without limit, but they cannot be directly compared or used in calculations.
  • #1
Amany Gouda
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in the dispersion relation of the surface plasmon

the wavelength is proportional to square root of n. according to equation 5 in this paper:
https://Newton.ex.ac.uk/research/emag/pubs/pdf/Barnes_JOA_2006.pdf
if n goes to infinity, then what will be the value of wavelength.
Thank you
 
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  • #2
I don't see any n that could go to infinity in equation 5, and if you let one of the ε go to infinity (keeping the other constant) the square root has a finite limit.
 
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Related to If n is infinity, wavelength is equal to what?

1. What is the relationship between n and wavelength when n is infinity?

When n is infinity, wavelength becomes infinitely small or zero. This is because as n increases, the frequency of the wave increases, causing the wavelength to decrease.

2. How does the concept of infinity affect the wavelength of a wave?

When n is infinity, the wavelength becomes infinitely small. This is because infinity is a concept that represents something without limit, and as n approaches infinity, the wavelength becomes smaller and smaller without ever reaching a definite value.

3. Is there a specific formula for determining the wavelength when n is infinity?

Yes, the formula for wavelength is λ = c / f, where λ is the wavelength, c is the speed of light, and f is the frequency. When n is infinity, the frequency becomes infinitely large, causing the wavelength to become infinitely small.

4. Can the wavelength of a wave ever truly be zero?

No, the concept of zero wavelength is only theoretical and cannot be achieved in reality. As the frequency of a wave approaches infinity, the wavelength becomes infinitely small but never truly reaches zero.

5. How does the concept of infinity in waves relate to the concept of infinity in mathematics?

Both concepts of infinity represent something without limit or end. In waves, as n approaches infinity, the wavelength becomes infinitely small, while in mathematics, as numbers approach infinity, they become infinitely large. However, it is important to note that these concepts are not interchangeable and cannot be directly compared or used in calculations.

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