Synthetic fibers are known to display what property due to their crystalline structure?

Synthetic fibers exhibit birefringence, which is the property of exhibiting different refractive indices in different directions due to the crystalline structure of the fibers. This characteristic results from the arrangement of the polymer chains in the synthetic fibers, which can create an anisotropic optical property. When light passes through a birefringent material, it splits into two rays, each traveling at a different speed, depending on the orientation of the birefringent material with respect to the light. This phenomenon is particularly useful in forensic analysis for the identification and comparison of fibers under polarized light microscopy.

The other properties listed do not specifically stem from the crystalline structure of synthetic fibers. Flexibility refers to the ability of a material to bend without breaking and is not directly related to crystalline properties. Opacity means the material does not allow light to pass through, and translucence means it allows some light but not detailed images to pass. Neither of these optical properties is influenced by the crystalline structure in the same way that birefringence is.