Real depth and Apparent Depth

Real depth and Apparent Depth :

When an object is placed in a denser medium, it appears to be raised. 

         

To find the apparent depth, consider an object O placed in denser medium, say, water at a distance u from the surface XY. A ray of light OA incident normally on the surface of separation passes into air along AA' without suffering refraction.

Another ray OB incident at B at an angle i is refracted along BC away from the normal making an angle r with the normal NB. The ray CB when produced backward will meet OA in I.

                                       To an eye looking into the medium the rays BC and AA' will appear to diverge from I. The object O will thus appear to be raised to the point I, which is, therefore, the virtual image to the object O. 

If µ is the refractive index of water with respect to air, then 1/µ will be the refractive index of air with respect to water. Thus

            sin i / sin r = 1/µ

Now 

             ∠AOB = i     and      ∠AIB  = r

 or               1/µ  = sin i/sin r

                                          =  AB/OB   X    IB/AB

                                          = IB/OB

If B lies very close to A, then

OB = OA         and          IB = IA

1/µ = IA/OA

therefore,         µ = OA/IA = Real depth/ Apparent depth

                          = u/v

now                 µ > 1

∴                     u > v

Hence, the image of the object O appears to be raised to the position I.

Thus when an object is placed in a denser medium and is viewed through a rarer medium it appears to be raised. It is for this reason that the bottom of a tank filled with water appears to be raised.

Courtesy: engineeringphysics.blogfa.com

A Cyberphysics page