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?
[Physics] Why do the sides of the fish aquarium look like mirrors
geometric-opticsopticsreflectionrefraction
Related Solutions
The resolution of a regular photograph is limited by the size of the silver halide crystals in the emulsion, while the resolution of a computer image is limited by the number of pixels used to store it.
However, a typical telescope mirror has no structure bigger than the size of a grain boundary, and this is much smaller than the wavelength of optical light. In this respect there is no finite resolution comparable to a photograph or computer image.
The resolution of a telescope is limited by the size of the mirror rather than by any quality of the reflecting surface. The light reflected by the mirror is diffracted by the mirrors edges forming an Airy disk. This limits the angular resolution to approximately:
$$ \sin \theta \approx 1.22 \frac{\lambda}{d} $$
where $\lambda$ is the wavelength of light and $d$ is the mirror diameter.
You are getting reflections from the front (glass surface) and back (mirrored) surface, including (multiple) internal reflections:
It should be obvious from this diagram that the spots will be further apart as you move to a more glancing angle of incidence. Depending on the polarization of the laser pointer, there is an angle (the Brewster angle) where you can make the front (glass) surface reflection disappear completely. This takes some experimenting.
The exact details of the intensity as a function of angle of incidence are described by the Fresnel Equations. From that Wikipedia article, here is a diagram showing how the intensity of the (front) reflection changes with angle of incidence and polarization:
This effect is independent of wavelength (except inasmuch as the refractive index is a weak function of wavelength... So different colors of light will have a slightly different Brewster angle); the only way in which laser light is different from "ordinary" light in this case is the fact that laser light is typically linearly polarized, so that the reflection coefficient for a particular angle can be changed simply by rotating the laser pointer.
As Rainer P pointed out in a comment, if there is a coefficient of reflection $c$ at the front face, then $(1-c)$ of the intensity makes it to the back; and if the coefficient of reflection at the inside of the glass/air interface is $r$, then the successive reflected beams will have intensities that decrease geometrically:
$$c, (1-c)(1-r), (1-c)(1-r)r, (1-c)(1-r)r^2, (1-c)(1-r)r^3, ...$$
Of course the reciprocity theorem tells us that when we reverse the direction of a beam, we get the same reflectivity, so $r=c$ . This means the above can be simplified; but I left it in this form to show better what interactions the rays undergo. The above also assumes perfect reflection at the silvered (back) face: it should be easy to see how you could add that term...
Best Answer
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".