get some goggles, a ladder, and towel. Dunk your head in upside down and find out. haha.
But in all honesty, it depends on the lighting and the way it reflects through the water... Who remembers prisms from 8th grade science.? Its all about lenses and the way that light and images travel through the water column -> glass/acrylic -> your eyes.
Heres basic info how eyesight works= Light is projected from a source (ex the sun) it is projected to an object (tree) the light bounces off the object enter the cornea (first lens in eyeball & in front of pupil aka the "dark hole") when the light mixed image enters the cornea it is inverted where it is re-projected on the back of your eye (aka retina). The retina process the combination of light, colors, shape. and sends the message through your optic nerve to the brain. The image is then processed and reverted back to the original position (aka upright position).
Now that we know that, Heres the best way i can describe light and reflections: imagine you are standing in your living room at 11pm and looking outside the sliding glass door. When the lights in the room are OFF, you can clearly see through the object (aka glass) and see things like trees, patio furniture, axe murderer. When you turn the lights ON in the room, you can no longer see said murderer, all you see is a reflection of your pretty self and everything inside the room.
Heres the science: First off- understand that our eyes, much like camera lenses will attempt to absorb as much light as possible to produce a clear image off of whatever it can. This means, you will recognize objects that are in brighter/ more intense lighting before you recognize the other less well lit objects. (Ex: when camping you see flashlights, BEFORE you can make out the body shape of the person carrying it)
Remember when we said that light REFLECTS off solid objects (the tree) and projects into our eye? well.. if there is MORE light inside than outside the glass window, your eye will first process the most intensely lit obejcts which happens to be the objects that are behind you in the room, thus a reflection is born. If the room is DARK, your eye cannot clearly process the indoor light and objects in the room, so it looks beyond the glass for the next best source of light, which is beaming from the Moon/ outdoor lights -> axe murderer-> through the glass (Remember, because there is not enough light inside) -> into your cornea, and we all know the rest.. freak out and adrenaline ensues because you have a weirdo in your backyard with an axe.
How it relates to fish tanks: If the lighting inside the tank is on, we can assume it is brighter/more intense than the lights outside the tank (ambient room lighting). Thus, we or the fish will FIRST process the objects that are better lit inside the tank. This creates a reflection... Of everything. Thats why the divers can see themselves and sharks behind them(see above post for mention). Therefore, yes when the lights are on your fish see a reflection of the tank and its inhabitants When the tank lights are off, the objects in the room are better lit, so they stand out the best, and the fish will no longer see themselves, they just see some dummy staring back at them. as well as whatever else is going on in the living room, like you picking your nose on the couch.
So why does a fish react to my finger outside the glass?
1. If the DT lights are off, he can see it clear as mud. and you just look like loser waving your finger around in the middle of a room.
2. if the tank lights are on: When you stand 4ft from the tank and wave you finger around at the tank they dont react... why? because the lighting inside the tank is more intense than the lighting on your finger. Remember, they see the most well lit objects first. However, as you press your finger on the glass (outside the tank) the lighting inside the tank is intense enough to penetrate the glass, bounce off and light up your big fat finger and still intense enough to project an image back to the fish's eye.
Super long story short: DT lights on? yes they see themselves. DT lights off? No they do not necessarily see their reflection. It just depends on the intensity of the lighting surrounding the objects.
Phew... Clear as mud?