# Decomposition of the wave-vector in terms of wavelength

• watty
In summary, the conversation discusses a problem in relativistic optics that involves finding k_x, k_y, and k_z in terms of lambda, c, and theta. The individual started off using trigonometry to express k_x and k_y, but is unsure how to express k_z without introducing an angle between the x and z axis. The person asks for help and is advised to set k_z equal to 0.
watty
Im attempting a problem in relativistic optics that's asking me to write k_x, k_y and k_z in terms of lambda, c, and theta (theta being the angle between a source and an observer, at rest relative to each other). Lamda is the wavelength in this reference frame. I started off using trigonometry to say that { k_x = 2*pi*cos(theta) / lambda } and equivalent but with sin(theta) for k_y but then how do I express k_z ? i can't see homework to it without introducing an angle between the x and z axis!

Hi watty!

(have a theta: θ and a lambda: λ and a pi: π )

uhh? you're in charge!

so just put kz = 0.

## 1. What is the definition of "decomposition of the wave-vector in terms of wavelength"?

The decomposition of the wave-vector in terms of wavelength is a mathematical approach used to break down the wave-vector into its constituent parts, specifically in terms of the different wavelengths present. This approach is often used in the study of waves, such as electromagnetic waves, sound waves, and water waves.

## 2. How is the wave-vector decomposed in terms of wavelength?

The wave-vector can be decomposed in terms of wavelength by using the wave-vector's magnitude and direction, as well as the wavelength of the wave. The magnitude of the wave-vector is equal to the wave's frequency divided by its speed, and the direction is determined by the orientation of the wave. By factoring in the wavelength, which is the distance between two consecutive points on a wave with the same phase, the wave-vector can be decomposed into its constituent parts.

## 3. Why is it important to decompose the wave-vector in terms of wavelength?

Decomposing the wave-vector in terms of wavelength allows for a better understanding of the properties and behavior of waves. By breaking down the wave-vector into its constituent parts, we can analyze and compare the different wavelengths present in a wave, which can provide insights into the wave's speed, frequency, and direction. This approach is particularly useful in the study of complex wave phenomena, such as interference and diffraction.

## 4. Are there any limitations to decomposing the wave-vector in terms of wavelength?

While decomposing the wave-vector in terms of wavelength is a useful tool in the study of waves, it does have its limitations. This approach is most effective for waves with simple and regular patterns, and may not accurately represent more complex wave phenomena. Additionally, this method does not take into account the wave's amplitude, which can also affect its behavior and properties.

## 5. How is the decomposition of the wave-vector in terms of wavelength used in scientific research?

The decomposition of the wave-vector in terms of wavelength is a fundamental concept in the study of waves, and is used extensively in various fields of science and engineering. This approach is particularly important in fields such as optics, acoustics, and seismology, where understanding the behavior of waves is crucial. Additionally, this method is also used in the development of new technologies, such as fiber optics and ultrasound imaging.

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