# Understanding Coherent Length & Interference Effects

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In summary, coherence length refers to the spatial length over which there is a specific phase relation among different frequencies in a wave's spectrum. This is also known as coherence time, which is the time it takes for different frequency components to be out of phase by a specified amount. Only coherent waves show an interference pattern, as incoherent waves do not have well-defined maxima and minima. The order of magnitude for coherence length and coherence time can vary depending on the specific situation and is related to the spectral bandwidth and apparent size of a source.
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What is coherent length?
and how it is affected interference

Okay, all real waves have a continuous spectrum of frequencies. Different frequencies drift out of phase with time. The coherence time is the length of time it takes for different frequency components to be out of phase by some amount - typically one eighth or one quarter of a cycle.

Only coherent waves will show an interference pattern. Incoherent waves will not because they don't have well defined maxima and minima.

Claude.

AFAIK, coherence length is the spatial length over which there is a specific phase relation among the different frequencies of the spectrum, while out of that length the phases are casual.

Thanks. but usually what is the order of magnitude of coherent length as well as coherent time?

The coherence "length" is taken to refer to the maximum path difference in an unequal-arm interferometer, and thus actually refers to the coherence time (L = c*t), which is given by the spectral bandwidth.

The coherence "area" refers to spatial coherence and is related to the apparent size of a source.

That's why I tend to be explicit when discussing this stuff in class- temporal or spatial coherence.

## 1. What is meant by coherent length?

Coherent length refers to the distance over which a wave maintains its phase relationship, or coherence, with itself. In other words, it is the distance at which a wave can interfere with itself and produce a stable interference pattern.

## 2. How is coherent length related to interference effects?

Interference effects occur when two or more waves overlap and interfere with each other. The degree of interference depends on the coherent length of the waves. If the waves have a long coherent length, they will interfere more strongly and produce a more defined interference pattern.

## 3. What factors affect the coherent length of waves?

The coherent length of waves can be affected by several factors, including the frequency and wavelength of the waves, as well as any medium through which the waves are traveling. In general, waves with shorter wavelengths and higher frequencies have longer coherent lengths.

## 4. How is coherent length measured?

Coherent length can be measured by performing interference experiments and observing the distance at which a clear interference pattern is no longer visible. It can also be calculated using the formula l = c/Δf, where l is the coherent length, c is the speed of light, and Δf is the frequency bandwidth of the waves.

## 5. What are some practical applications of understanding coherent length and interference effects?

Understanding coherent length and interference effects is crucial in various fields, including optics, acoustics, and telecommunications. It is used to design and improve technologies such as lasers, fiber optics, and wireless communication devices. It also has applications in medical imaging, astronomy, and quantum mechanics.

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