While comparing Goethite and Dioptase physical properties, the important data you should know is its chemical composition. Since chemical formula defines the molecular structure of the crystal, most of the physical properties like color, tenacity, solubility are governed by Goethite and Dioptase chemical formula.
Another important criteria for qualitative analysis of gemstones is Goethite and Dioptase Specific gravity. Specific gravity is the relative density of a gemstone compared with respect to density of water. Gemologists use Goethite and Dioptase Optical Properties during the identification of gemstone. Specific gravity of Goethite is 3.25-3.35 whereas that of Dioptase is 3.25-3.35.