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Refraction: Real and Apparent Depth
To an observer standing at the side of a swimming pool, objects under the water appear to be nearer the surface than they really are.
A similar effect can be seen when looking through glass or any other transparent substance.
The effect is due to refraction of light at the boundary between the two media.
 
Consider the situation shown below, in which a person is looking at a fish in a pond.
 
 
Light leaving a point on the fish is refracted at the water/air boundary so as to appear to be coming from a point vertically above the real position of the fish.
The refraction creates the illusion that the fish is at a nearer the surface than it really is.
 
The refraction produces a virtual image of the fish above the real position.
 
The image is described virtual because it is formed at a place where there is no light from the object, the light just appears to be coming from that point.
 
 
 
   
  For the same reason, a straight stick observed when it is partly under water appears to be bent as shown here.
   
  (You have to take my word that it really is straight... would I lie to you?!)
   
 
The magnitude of this effect depends on the refractive indices (see refractive index) of the substances through which the light travels.
Consider again the case of the person watching the fish, shown in more detail below.
 
The real depth of the fish is R and its apparent depth is A.
It is clear that
and
as shown here, we can write
 
If i and r are small angles then sini=tani and sinr=tanr.
Therefore, we have
which means that
 
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