1. The problem statement, all variables and given/known data This is a multi-part problem. Visible light spans a range of wavelength between 0.4-0.7 nm, corresponding to a photon energy between about 1.8 and 3.1 eV. (a) An old practical test says that if you can see through a piece of material, it is almost certainly a good insulator. Why? (b) Why the modifier "almost"? How can a transparent material fail to be a good insulator? Hint: You can see through NaCl if you squint, but it is not a very good insulator. (c) On the other hand, there are many good insulators that you cannot see through, including both opaque ceramics and brightly colored plastics. Describe at least one possible microstructure that creates an opaque insulator. (d) Alvin, a random undergraduate of great academic promise, got a summer job with a technology company. He was assigned to the mail room. While inspecting incoming materials, he came across a box labeled optical fibers, which were metallic gray in color and totally opaque. He sent them back as rejects. His boss fired him, saying, "The fibers you returned were super-high-tech fibers for use with our hot new semiconductor lasers, and were desperately needed. They are exceptionally clear and transparent." What was Alvin's mistake? 2. Relevant equations None. 3. The attempt at a solution I read this https://www.physicsforums.com/showpost.php?p=899393&postcount=4 [Broken] but I don't think it's the model my teacher uses. (a) Since emitted light is caused by electrons moving from high energy states to low energy states across a band gap, if it is transparent it means the band gap is larger than 3.1 eV. Since the band gap is so large electrons cannot cross from the valence band to the conduction band. What I want to know is, what happens when the energy gap is less than 1.8 eV? I know if there is no band gap, the material is a conductor and the appearance is metallic. But shouldn't it be transparent as well? I suspect it has something to do with the post I linked at the top, but I don't know how. (b) Because NaCl is an ionic conductor, it does not conduct by electrons, but whole ions, which are unrelated to opacity. (c) This question is the one I'm having the most trouble with. The only thing I can think of is that the plastic absorbs light at a high frequency (above visible) and emits light at a lower, visible frequency. (d) The "hot new semiconductor laser" emits light that is in the infrared, so the fibers do not need to respond to visible light.