Final answer:
Obsidian, due to its glassy texture, would make the best mirror when polished among the given minerals because it can produce a highly reflective surface, unlike calcite, hematite, or pyrite.
Step-by-step explanation:
Given that quality mirrors reflect a great deal of light, the best choice among the given minerals for crafting a mirror when polished would be obsidian. Obsidian has a smooth, glassy texture and can produce a highly reflective surface, ideal for mirror making. On the other hand, minerals like calcite may exhibit properties like double refraction, which is undesirable for mirror surfaces as it would produce multiple images. Hematite and pyrite, while they can be shiny, do not match the smoothness and clarity required for the reflection quality of a good mirror. Furthermore, pyrite, although it has a metallic luster, is not as smooth and reflective as obsidian when polished.
Using the law of reflection, we understand that the smoothness of a surface is key to creating a sharp image. Since sandpaper would make a mirror's surface rough, it is not suitable for polishing a mirror if a clear reflection is desired.
A perfectly reflective mirror that reflects all the light that falls on it can be achieved using total internal reflection, which is an aspect of refraction where light reflects entirely within a medium rather than passing through it. This is seen when the index of refraction for the medium the light is entering is less than the medium it is passing from, which isn't a specific attribute of any one of the listed minerals but rather a concept in physics.