Hello, Guadalupe,
I'm having a little difficulty answering some of the questions, but I'll make a few comments.
a. Under what circumstances would you be able to conclude that the questioned and known glass samples did NOT have a common origin based only on these density and refractive index analyses?
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Based just on the measurements alone, I don't see a way to reasonably conclude the chips do NOT have a common origin. If we are allowed to consider other properties, such as surface coating, crystal structure, etc., then perhaps evidence could be found proving they did not have a common origin.
b. Under what circumstances would you be able to conclude that the questioned glass may have originated from the known glass from the burglary based only on these density and refractive index analyses?
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Again, can we consider additional data? If the chip can be matched to a piece of the original window, then that may be enough evidence. It would help to have density and refractive index values from a wide range of glass samples to see what differences might exist, and analyze the data to determine the whether the precision of the measurements can confirm a similarity exists.
c. Is it possible to conclude that you have individualized the questioned glass chip to the known glass from the burglary based only on density and refractive index analyses?
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Not unless we have a comparison to other glass samples not connected to the crime scene to determine the liklihood that the density and refractive index data are indeed distintice, using a correlation statistic.