Why does a duck appear split in half when viewed at an angle through water?

[sc3103]

Suppose that you look at an aquarium with your eyes at the lever of the water surface. A duck swims on the surface of the water. When you look at the duck from the front, everything seems normal. However, when you look at the duck at an angle to the glass surface, the duck seems to be spilt in half, with the feet paddling ahead of the upper body. Explain this phenomenon.

(I know this has to do with refraction, but how can I explain that?)

Suppose that both the duck and your eyes are at a distance of 1m from the glass, and the line connecting them forms a 30 degree angle with the glass. Calculate the difference between the directions of the line of sight of the upper and lower halves of the duck.

(I know I am not following the rules very well, but I am really not understanding this phenomenon.)

 

[mezarashi]

The phenomena arises from the idea that your eyes cannot tell whether light that reaches it has gone through refraction or not. It assumes a straight line path. That's also why there appears to be a virtual world in a mirror.

To the physics of it. You can use Snell's law to determine the change in angle with air being n = 1, and water approximately n = 1.5 if I call. Draw the ray going from the duck to your eyes. Then trace the ray backwards the same distance in a straight line (i.e. as if there was no refraction). This is where your eyes think that part of the duck is.

 

[lightgrav]

You can't tell where the virtual image is (where the duck "appears to be")
unless you draw 2 rays, slightly diverging, from the same place on the duck.
Suppose one goes in one eye, the other ray into your other eye.
Your brain looks back along those rays (knowing where eyes point).
YOU trace the two rays backwards (undeflected) to see where they cross.
Snell's Law leads to a simple small-angle formula for apparent depth.

Water has index of refraction of about 1.33 (ignore the glass).