Multiple wavelengths of light through much larger single slit

[littlepapa87]

A text I am reading noted that as a multichromatic light source (consisting of many individual peaks) is passed through the my slit (order .25mm) the peaks will be spread over the neighboring wavelengths in a roughly Gaussian distribution. I am trying to understand why this is, and how I would go about finding the FWHM of the spread in wavelength space.

my application for this is Raman spectroscopy. For my work the light is scattering at 580nm 607nm along with a few others for vibrational transitions, and from 532-560ish for rotational transitions.

 

[Valerie Park]

The reason why the peaks spread over neighboring wavelengths in a Gaussian distribution is due to diffraction. When light passes through a very small slit, it is diffracted and spreads out in a Gaussian distribution. This is because when a wave is passed through a narrow slit, the waves interfere with one another and create a pattern of constructive and destructive interference. The constructive interference creates a peak in the middle, with the surrounding regions showing decreased intensities due to the destructive interference. To find the FWHM of the spread in wavelength space, you would need to calculate the Full Width at Half Maximum (FWHM) of the Gaussian curve. You can do this by finding the half maximum points on either side of the peak, and subtracting their values. This will give you the total FWHM for the peak. In order to apply this to Raman spectroscopy, you would need to determine the FWHM of the peaks at each of the wavelengths you are measuring (580nm, 607nm, etc). This can be done by calculating the FWHM of the Gaussian curve at each of these wavelengths. Once you have determined the FWHM for each of the peaks, you can then use this data to analyze the vibrational and rotational transitions.