You can get a plastic DSLR camera body cap for less than 50 cents each (ebay from China). This cap goes where the lens would attach the camera when you don't have a lens on. Sometimes I cut a hole in the center of a cap and make really hacky camera "lenses" for fun. You could put a prism on the outside of a cap.
You would then need to calibrate your new spectra-cam on something with a known radiation (usually just find a good blackbody radiator.) You can't just convert to black and white without calibration because the RGB sensors on the camera are going to have their own sensitivity to different wavelengths. This would be an awesome project!
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I write firmware for high end professional LED lights, and have a $3K spectrometer on my desk. Here are things I've learned:
1. CRI is simply a bad formula to judge light quality overall and gives almost meaningless results at lower color temperature levels.
2. There are lots of fantastic python modules for working with spectrograph and light data.
3. One awful thing cheap LED lights do is blink slowly to control their voltage. This is at least as bad a poor CRI for aggravating your eyes. (Sometimes you can see this just by using slow motion video on your phone)