Calculate the coherent length of this LED

AI Thread Summary
The discussion revolves around calculating the coherence length of an LED with a center wavelength of 940 nm and a width of 30 nm. The coherence length, L, is derived from the formula L = C * (λ^2 / Δλ), where C is typically around 0.5, although the user initially used C = 1. The importance of significant figures is emphasized, noting that the final answer should reflect the data's precision, which is given to two significant figures. The conversation highlights the variability in coherence length calculations based on the chosen formula and the need for proper rounding in academic submissions.
nao113
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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
Screen Shot 2022-06-08 at 16.56.06.png

Answer:
Screen Shot 2022-06-08 at 16.56.11.png
 
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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
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’!
 
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’!
so the answer will be 14726.7 nm?
I got the reference from my class material like this pic
 

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nao113 said:
so the answer will be 14726.7 nm?
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.
 
Steve4Physics 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.
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
 
nao113 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
Can you tell me what your Post #1 and Post #3 answers are when correctly rounded to the appropriate number of significant figures? If you are not sure how to do that, at least try! If wrong, I will help.

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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