The world above the water, as seen by a fish

Applet by Fu-Kwun Hwang

When light propagates from one medium into another, its speed changes, which causes the light to reflect and refract at the boundary.

The index of refraction of water is 1.33 (4/3). As light travels from water to air, it will bend away from the line perpendicular to the surface. When the incident angle is greater than 48 degrees, all the light is reflected back into the water (total internal reflection).

As your pet goldfish in the aquarium looks up, it will see a reflected view of the sides and bottom of the aquarium beyond the 48 degree angle, while directly above, it sees a compressed view of the outside world.

The refraction of light is responsible for many illusions:

The shape of a thing you see under the water surface is different from what it really is.
A submerged object appears to be nearer the surface than it actually is.
This java applet lets you see the view as seen by your fish, looking up at you. Pretty weird!

Instructions on how to use the animation below:

Usage: The area is divided into two regions. The light gray area is the air above the water surface. The green area is below the water surface. A fish with two eyes is under the water surface.

All the light from the world above the water surface that the fish can see enters the water through yellow region.

The cyan colored block is an object above the water surface. The blue polygon is the image of the block.

The light path for each corner of the object is shown by the light gray lines. The yellow lines indicate where the object appears to be, to the fish. As you will discover, the fish sees the world in very distorted form.

Click one of the corners of the cyan block with the left mouse button to view light paths for that point.
Click near the center of the block with the left mouse button and drag the mouse to move the object.
Click the right bottom corner of the block with right mouse button and drag the mouse to change the size of the object.
Move the object from left to right/up and down/change its size, and watch how the image changes. Click on one of fish's eyes and drag the mouse button (left/right) to change the location of the eye.

It's fun! Play with it! Think about it! Fish have to understand this! Enjoy the fun of physics.

Fill a glass with water and look at objects beneath the surface. Try it!