Calculate the coherent length of this LED

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
Screen Shot 2022-06-08 at 16.56.06.png

Answer:
Screen Shot 2022-06-08 at 16.56.11.png
 
Physics news on Phys.org
  • #2
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’!
 
  • Like
Likes berkeman
  • #3
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
 

Attachments

  • Screen Shot 2022-06-08 at 23.29.26.png
    Screen Shot 2022-06-08 at 23.29.26.png
    20.1 KB · Views: 105
  • Like
Likes Delta2
  • #4
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.
 
  • Like
Likes Delta2
  • #5
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
 
  • #6
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>​
 
  • Like
Likes nasu

Suggested for: Calculate the coherent length of this LED

Back
Top