Question

When you look through a fish tank at someone on the other side, you only see a reflection of the fish in the tank. However, the other person can see you clearly. Explain.

Answer 1

Their is a phenomenon in Electromagnetic waves, called Total Internal Reflection (TIR).

The equation for snell's law [sin(a1)/sin(a2) = v1/v2 = n2/n1] which relates the angle between the light ray in the two mediums which they make with the normal common to both medium (a1 and a2) and the velocity of light in two mediums (v1 and v2) and the refractive indices of the two medium (n1 and n2). this refractive index is a property of the medium which is fixed for them irrespective of how the light enters it, as long as its the same medium. for example for water its value is: 1.33. now when light enters a medium with lower refractive index medium, say air, to higher refractive index medium, say water. then the light bends towards the normal, if their is some angle between the incident ray and the normal, but if not both a1 and a2 are zero and the light passes right through. Thats why the opposite side is seen same as with with water as without water.

Now consider this if the light ray comes from an angle almost 90 degree with the normal, it will get bent to some angle when entering the water. this angle is a special angle for these two mediums. this will be sin(90)/sin(a2) = 1.33/1

sin(a2) = 1/1.33 = 0.7518
a2 = 48.753 degree

now consider the opposite scenario when the light ray is coming from the water and going to the air. if you think about it, because of the reverse symmetry in light ray geometry the path that light travels will be symmetrical, up until this angle (48.753 degree) at which the light will come out in the air almost perpendicular to the vertical normal in the figure. but increasing this incident angle in the water to say 50 degree will result in Total internal Reflection. the light ray will reflect back and will not go in the air. This is what happening with the adjacent sides of the fish tank. the angles from you see the adjacent sides are more than 48.752 degree and because of the light going in get Reflected back instead to going into the air.