But yes, you're right that shiny things tend to seem darker from most angles, because the observer is usually not in line with most of the reflected light.
In computer graphics, Blinn highlights are a pretty decent approximation for shiny surfaces. (Interestingly, the highlights generally don't take on the color of the object unless it's metallic.)
https://en.wikipedia.org/wiki/Blinn%E2%80%93Phong_reflection...
Car headlights on wet pavement are kind of a worst case. You don't get much benefit from your own lights because the vast majority reflects off at a useless angle, but it does reflect back up at oncoming traffic.
(Impractical startup idea: headlight drones, that fly ahead of your car in rainy weather and illuminate the road in front of you from a more useful angle. Powered by microwaves beamed from the car.)
Reflection on the surface of the water is "free" both ways (from air to air bounce, and from water to water bounce), no energy loss. Travelling through water - similar, lite energy loss, though not exactly zero. The only way we can really lose energy is on the cloth reflection. Therefore (almost) all of the darkness effect should be attributable to increased number of cloth reflections, via the total internal water reflection mechanism.
This also explains why colors are more vivid when the cloth is wet - after all the same ray of white light bounces off the cloth several times, increasing the "color filtering properties" of the cloth.
Apart from index mediation, the water film does something else. For rough/fibrous surfaces, the reflection will be diffuse, i.e. visible from all directions. When a water film is present, the surface becomes smooth, and the reflection will be specular, and only visible in one direction. So in most directions, the material will appear darker.
Conductors are a completely different beast. The reflection off of metals are not solely dictated by the refractive index.
Yes, that's precisely the part I was addressing in my last paragraph. If it's specular reflection, then in "most directions" it will appear darker, as you say, but in one direction it should appear brighter, even shiny. But I've never seen a damp rag be shiny in any direction.
(...and it shouldn't be that hard to see, if that effect is really true. With any other shiny object (polished car, CD, balloon) you see the specular reflection frequently.)
The surface of a cloth is still much less smooth than a polished car, cd, etc, so is it possible that the specular reflection happens, but at a contrast that is too low for our eyes to detect, or in enough disjoint sections that we can't perceive it as a single effect?
There are plenty of phenomena that fall out of the range of our unaided perception.
We would, however, probably observe the specular reflection of instead of water we used a thicker transparent liquid, like clear glue.
> Before water is spilt, 100% of the light travelling towards that part of the shirt will hit the surface. But now only a fraction of the light moving towards it will hit its surface. This is because the light now has a layer of water to go through. And due to the reflectance of water, not all light at the air-liquid-interface (border between air and water) goes through the water. Some of it is reflected.
This is not clear, or at least needs another step. It is saying that part of the reason the shirt looks darker is because some of the light never had a chance to reflect off the shirt, because it reflected off the water first. But the observer only cares whether light is reflected at all, not whether it reflected off the shirt or the water.
I assume the unwritten part is that this specular reflection is only reflecting light in one direction, instead of diffusely, so if the observer is not in that line of reflection, they won't see the light. But this explanation seems wrong to me, as it implies that a wet shirt will have some brighter highlights at some angles, and yet I have never seen this.