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

this can be explained on the phonomenon Total Internal reflection

The equation for snell's law sin(T1)/sin(T2) = 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(T2) = 1.33/1

sin(T2) = 1/1.33 = 0.7518

T2 = 48.753 degree

------------------------

but on the other side

when the light ray is coming from the water and going to the air.

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.