Question #e59b8

when we see the stone from glass side it seems to be raised.this is due to refraction of light.since light travelling from glass (water) to air suffers deflection in path of light.

Assume an object is at point #X# and we look at it (that is, we sense the light reflected by this object) using our two eyes at points #E_1# and #E_2#. The object reflects light in all directions, but we catch in our eyes only rays directed along the straight lines from object to eyes, one eye catches the light reflected by an object along line #XE_1#, another - along #XE_2#.

The distance to the object, as we estimate it, depends on the angle #/_E_1XE_2#. The smaller this angle - the greater the distance to an object. So, our brain converts the position of our eyes in the sockets (or, it can be expressed as the tension of muscles that control the position of the eyes) into distance.

The eye muscles are not tense when we look straight forward at an object extremely far away, like a horizon, and the angle #/_ E_1XE_2# equals to zero. The more tense the eye muscles are - the closer our eyes are focused on an object, the greater is the angle #/_ E_1XE_2#, and the smaller is the distance to an object as estimated by a brain. Not a simple task!

Consider now an object is in the water. The light reflected by this object changes its direction when crosses the water/air boundary at some angle. If an angle of a ray of light with a perpendicular to this boundary is #alpha# on the water side, it will be #beta# on the air side. This is related to a different speed of light in different environments. When goes from water to air, the angle to a perpendicular to a boundary surface is increasing: #alpha < beta#.

Considering this, rays of light directed along straight lines between an object at point #X# under water and our eyes at points #E_1# and #E_2# will not fall into eyes. Instead, different rays will. The ray that falls into #E_1# will travel from #X# to #A_1# point on the water surface, then to #E_1# in the air, and the line #XA_1E_1# is not straight. The angle between #XA_1# and perpendicular to a surface at point #A_1#, #alpha=/_XA_1P_1#, will be smaller than the angle between #A_1E_1# and this perpendicular, #beta=/_E_1A_1Q_1#. So, our eyes must focus closer, based on directions from #A_1# to #E_1# and, similarly, from #A_2# to #E_2#. So, the object appears at point #Y#, that is closer to eyes than the real location of an object #X#.

But our brain senses only the position of eyes to estimate the distance. Greater tension of muscles is interpreted as closer distance. That's why we think that the object under water is closer than it really is.

Here is a diagram I drew of this:

The stone emits light in some direction, and our eyes send and collect light rays from some direction. When we look into a tub of water, our eyesight path is tricked into believing the stone is higher than it actually is because the index of refraction of water is higher than that of air or a vacuum (#~~1.33# vs. #~~1.00#).

This higher index of refraction bends the path of a light ray more towards the normal (perpendicular/normal to the surface of the water), and if our eyes knew that ahead of time, they would know where the stone was. However, we perceive our eyesight path to keep going straight without bending as we look through a denser medium, and we believe the stone is higher than it actually is.