We measuredthe refractive index of silk foam. Because of it's high porosity, we found a refractive index of 1.06 very close to that of air. I guess cotton would show similar values very close to 1 (if its porous).
Otherwise, you can also check our review on THz imaging. Specifically, section 2.2 where we show how to calculate refractive index from transmission/reflection measurements. Here: