I was recently at a Sea Life Center and took a lot of photos there. The following image is from a fish tank which has cylindrical shape. What is the rainbow-effect at the surface of the glass called? Why can I see it through the camera, but not with my eyes? (Or at least not that clearly)?
When glass has stress, which can be induced and/or reduced through thermal or mechanical processes, it is visually revealed through the use of light in conjunction with a specifically oriented polarized filter. Such instruments are called a polariscope.
Stress is a molecular imperfection within the structure of the material, which causes slight variations and inconsistencies affecting the index of refraction. Often this cannot be seen with the naked eye, but through the utilization of linear and circular polarizers. This invisible phenomenon is revealed as bright light patterns, distortions, and color.
Toughened glass is safety glass, and it is used when more strength is needed than normal glass will provide. We are talking about glass used in passenger vehicles, bulletproof glass, diving bell and diver mask, architectural glass etc. Safety glass is tempered using heat plus ingredients chosen to add strength. The large fish tanks of the aquarium are constructed using this type of glass.
What happens is, the glass has different indexes of refraction on a spot by spot basis. Scientists use a polariscope to view and inspect the glass. When examined via polarized light, the stress points are clearly visible as circles or ovals surrounded by a rainbow of colors.
Likely your camera had a polarizing filter mounted. We do this when imaging objects that are on the other side of a glass pane. If no polarizing filter was mounted, the optics of your camera nevertheless induced this phenomenon.
Does your camera have a polarizing filter on it? This looks like stress induced birefringence.
How is the rainbow-effect at the surface of the glass called?
Refraction. It's the same thing that happens when light passes through a prism, or a lens, or really any time light passes from one medium to another with a different refractive index. Basically, light changes direction when it passes from one medium to another, and the amount of change is a little different for different wavelengths. The different degree of bend for different wavelengths (i.e. colors) make "white" light separate into its component colors. In this case there are at least three different media: the water, the tank material (probably some sort of plastic like polycarbonate), and the air.
Why can I see it through the camera, but not with my eyes? (Or at least not that clearly)
Your camera probably had to use a somewhat long exposure (it looks like there's some motion blur in the fish) to compensate for the low light in the aquarium. That, and maybe a larger aperture and boosted ISO, might have amplified the rainbow that looked very faint to you.