While pictures taken through the periscope prism are interesting I always wanted to recreate the pictures taken by Vince Marinaro in his book "In the Ring of the Rise". The physics of how a fish "sees" the world above the water have been known, and explained, for well over a hundred years (see list at end of some references I used). Visualizing it is a different matter. Marinaro was the first to my knowledge to try and capture it on film.

I built a simple slant box, which I gave away, and took the following pictures. the first requires a bit of explanation. The two rocks you see are reflections; the rocks are actually sitting on the bottom of the box; you can see the tip of the larger rock in its actual location. The fly is floating on the water's surface.

In the next picture the wing is obvious. It is slightly distorted in height and, as you will see in subsequent photos, becomes more-so due to refraction. The light source is evident in the upper left of the picture.

In the third picture the wing appears detached from the fly and floating above it.

I'm building a new slant box and hope to post better pictures along with an explanation of the physics involved in the near future. Here's a picture of the new box:

Oct, 2022
I finally got around to expanding this. I'm sure you remember the refraction demo from your high school science class; a straw placed into a glass of water appears to be bent at the water's surface. The RI (Refractive Index) of air at sea level is 1.0003 and 1.333 for water. A gentleman by the name of Snell worked out the math and the result without all the gory details is that in our case (the fish in water peering out into our world) sees things very differently then we do. The fish sees our world as if peering through a variably sized port hole:

The size of the porthole depends on the fish's depth. Technicaly, the diameter is twice the angle (from the vertical) x depth where the angle is very close to 48.6°. But note that the fish "sees" the same amount of the outside world the only thing that changes for the fish is the area in which things will appear sharper and with less distortion.

But for the dry fly fisherman, the following is "close enough" for estimating where the trout can clearly see your fly.

There's quite some distorted height as the viewing angle approaches the water's surface, height becoming less the further the object is from the edge of the viewing window. Although this may seem similar to our vision, there's a major difference in that we would also see a decrease in the object's width; the fish does not. In other words the fish sees the object as squashed. Here's a crude diagram:

As the wing of the fly gets closer to the edge of the porthole it becomes taller and at the edge and becomes visually (to the fish) "attached" to the body. This is what you can see when you watch the video, but first take a look at the still picture below. The upper green circle is the wing of the fly note the it is apparently detached from the fly and is short in height. The fly's body is visible below as it is in the water and the trout can see it there. Ignore the two fuzzy areas, the one near the wing is a shadow and the other is the monofilament "tow line" I used to pull the fly across the water.

The motion starts about half way (10 seconds) through the short video:

And here's a video illustrating the wing coming closer and closer to the fly's body until they appear to join at the edge of the trout's visual port hole.

Similarly, as you're skulking along the far bank, not wanting to spook your pet trout "Charlie" and he recognizes your waders and decides to get a closer look by swimming over toward you. This animation attemts to show you what he "sees".

How the trout's brain processes this information is an unknown of course.

Some of the references I used are:
"The Amateur Scientist" by Jearl Walker Scientific American Mar 1984
"At the Edge of the Window" by Harmon & Cline, Rod & Reel v1,n7
"Angling Optics" by Fenner, Trout Spring 1990
"Stream Life with a Trout" by Whitlock, Trout Summer 2001
"In the Ring of the Rise" by Marinaro 1976