- #1

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- Homework Statement
- Calculate the coherent length of the following LED.

Center wavelength, λ= 940 nm Width, Δλ= 30 nm

- Relevant Equations
- I put the equation in the picture below

Answer:

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In summary, we have discussed the calculation of the coherence length for a LED with a center wavelength of 940 nm and a width of 30 nm. The formula used in the course is L = λ^2/Δλ, which gives a coherence length of 14726.7 nm. However, it should be noted that coherence length is sometimes defined with an additional factor of 1/2, resulting in a coherence length of 7363.3 nm. The correct answer will depend on which formula is chosen and the appropriate number of significant figures are used.

- #1

- 68

- 13

- Homework Statement
- Calculate the coherent length of the following LED.

Center wavelength, λ= 940 nm Width, Δλ= 30 nm

- Relevant Equations
- I put the equation in the picture below

Answer:

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- #2

Homework Helper

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Hi @nao113. You haven't actually asked a question! But a few thoughts anyway….nao113 said:Homework Statement::Calculate the coherent length of the following LED.

Center wavelength, λ= 940 nm Width, Δλ= 30 nm

Relevant Equations::I put the equation in the picture below

View attachment 302561

Answer:

View attachment 302562

Is Δλ the FWHM (full width at half maximum) or the half-width? Let’s assume it is the FWHM.

The coherence (not ‘coherent’) length, L, In a medium of refractive index 1 is given by:

##L = C \frac {λ^2}{Δλ}##

e.g. see https://en.wikipedia.org/wiki/Coherence_length

You have taken C=1 but typically C≈ ½. See above link.

You have been given data to 2 significant figures but your final answer has 6 significant figures - lose 1 mark in an exam’!

- #3

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so the answer will be 14726.7 nm?Steve4Physics said:Hi @nao113. You haven't actually asked a question! But a few thoughts anyway….

Is Δλ the FWHM (full width at half maximum) or the half-width? Let’s assume it is the FWHM.

The coherence (not ‘coherent’) length, L, In a medium of refractive index 1 is given by:

##L = C \frac {λ^2}{Δλ}##

e.g. see https://en.wikipedia.org/wiki/Coherence_length

You have taken C=1 but typically C≈ ½. See above link.

You have been given data to 2 significant figures but your final answer has 6 significant figures - lose 1 mark in an exam’!

I got the reference from my class material like this pic

- #4

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That would still lose a mark (even if correct) due to excess significant figures!nao113 said:so the answer will be 14726.7 nm?

However, from your attachment it appears that in your course, you are:

- using Δλ to mean the FWHM;

- using C=1 in the equation ##L = C \frac {λ^2}{Δλ }## (technically not correct, but never mind).

So, based on your course material, your original answer (in Post #1) would be correct if you rounded it properly.

- #5

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Thank you very much for your answer. Can you please tell me what the correct one is? Actually, I also tried this calculator https://www.calculatoratoz.com/en/coherence-length-of-wave-calculator/Calc-31767 and just like what you said it uses C = 1/2Steve4Physics said:That would still lose a mark (even if correct) due to excess significant figures!

However, from your attachment it appears that in your course, you are:

- using Δλ to mean the FWHM;

- using C=1 in the equation ##L = C \frac {λ^2}{Δλ }## (technically not correct, but never mind).

So, based on your course material, your original answer (in Post #1) would be correct if you rounded it properly.

- #6

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Can you tell me what your Post #1 and Post #3 answers are whennao113 said:Thank you very much for your answer. Can you please tell me what the correct one is? Actually, I also tried this calculator https://www.calculatoratoz.com/en/coherence-length-of-wave-calculator/Calc-31767 and just like what you said it uses C = 1/2

There is no single correct answer - it depends which formula you choose to use. If this is work to hand in, and I was the student, I would answer something like this:

Using the formula from the course (##L = \frac {λ^2}{Δλ }##) gives:

<Give working and correctly rounded answer>

However, it should be noted that coherence length is sometimes defined with an additional factor (typically ½), e.g. see (reference of Wiki article) giving ##L = \frac {λ^2}{2Δλ }##. This gives:

<Give working and correctly rounded answer>

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