I'm currently doing a lab in which we use a Michelson-Morley interferometer to analyse different light source. One of the mirrors in the interferometer is moved by a stepper motor. One of the light sources we use is a blue LED. Through a data collection programme, we build up an interferogram of the intensity of the light as it moves through the null point (with intensity on the y-axis and the amount of steps the motor has turned):
If we take a fast-fourier transform of this we will get a wavelength spectrum which looks like this:
We are then asked to calculate the coherence length and spectral width using the following formulae:
$\Delta \nu \times L =\tfrac{c}{2\pi}$ and $\Delta \nu =\Delta \lambda \tfrac{c}{\lambda ^2}$
Not much context was given in the lab script for these formulae, but from what I could gather, I thought $\Delta \nu$ referred to the spectral width, $L$ referred to the coherence length (?), $\lambda$ referred to the mean/peak wavelength and $\Delta \lambda$ refers to the full width half maximum of the wavelength spectrum (?)
Again, I'm not sure if I have interpreted that correctly, but assuming I did, the values I got for the coherence length and spectral width were as follows:
$L=1.12*10^-6$ and $\Delta \nu = 4.26*10^{13}$
They seem to be on the correct order of magnitude, but the reason I am unsure is that when I look at different light sources (e.g. a white LED), the wavelength spectrum has more than one peak, so I'm not sure how I'm supposed to determine the "mean wavelength" and $\Delta \lambda$ from those.