Why do the sides of my fish aquarium look like mirrors?

I bought a new fish aquarium which is square/cuboid in shape. My previous aquarium was spherical in shape. When I filled it with water and put the fish in two of them started acting very stressed so I was a bit worried. When I looked into the aquarium from the top, the sides of the tanks looked like mirrors under the water line. This caused me to worry that the sides of the tanks were mirrors to the fish and they could not see through the glass and into the room. Because of the stressed behaviour of the fish, I was almost convinced that this was the case and that the fish were in effect, in a prison made of mirrors. I tried to find a way of seeing into the sides of the tank like the fish so I put a mirror under the waterline and the mirror reflected the images of what was outside of the aquarium glass. So I thought that the mirror effect was an optical illusion but without putting my own head under the water and looking through the sides of the aquarium, I can't be 100% certain. Can anybody confirm if this is an optical illusion?

• To get the "fishes eye view", lower a mirror into the water and look directly down at the mirror from above, then manipulate the mirror to show you what is seen in various directions, The light will have to pass upwards through the water surface to your eyes, so the water will need to be still for this to work. Jun 13 at 23:30

There are two interfaces to consider - from the water into the glass and then the glass into the air. Light rays that are incident from water into glass will be partially reflected at any incidence angle if the refractive index of the water is less than that of the glass (quite likely).

The glass-to-air interface will partially reflect too, but there will be total internal reflection for light rays incident at greater than the critical angle, which has a value of $$\sin^{-1} (n_2/n_1)$$ (for $$n_2 < n_1$$), where $$n_2 \simeq 1$$ for air and $$n_1\simeq 1.5$$ for glass.

When you look into the tank from the top is it quite likely that you will see light rays that have been totally internally reflected from the glass-air interface, because you are looking down at an angle. This will give the walls a mirror like appearance when viewed at an angle greater than the critical angle. If you were to actually get the "fishes' eye view" you would be seeing only rays that have been reflected straight back. Only a small fraction of the light (a few percent) will be reflected back in this way.

One thing to note though is that if the tank contains a bright light and the room it is in is relatively dark, then even though only a small proportion of light from inside the tank is reflected from the glass walls, that small fraction may dominate over any exterior light passing through the glass from the outside - thus giving it the appearance of being mirror-like. This is the principle behind one way mirrors".

• Thanks for your answer. So does this mean that the fish can see through the glass if there is a light in the room ? Sorry,physics is not my subject and I am a concerned about the welfare of the fish.Thank you. Oct 8 '18 at 13:48
• @CatonawallRedhawk Roughly 95% of the exterior light will pass through the glass and into the tank. Depends exactly on the refractive indices and the angle of incidence. Oct 8 '18 at 15:26
• Rob Jeffries. Thank you so much for your replies.It has put my mind at rest now that I know that my fish can see into the living room and are not trapped in a 'prison'. I have also learnt something very interesting and useful.Thank you. Oct 8 '18 at 15:54