Real and Apparent Depth | Physics Grade XI

Real and Apparent Depth

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Real and Apparent Depth | Physics Grade XI

Real and Apparent Depth

Real and Apparent Depth
An object placed in denser medium when viewed from a rarer medium appears to be at a lesser depth than its real depth. It is due to refraction of light.

Real and Apparent Depth

Let a point Object O be at the bottom of the beaker containing water. Suppose XY is the plane surface which separates air and water.

A ray OA from O is incident normally to the surface XY and passes without bending along AD. Another ray OB is refracted along with C making an angle of incidence i and angle of refraction r. When seen from the top, the rays seem to be coming from I and, thus, object is seen at point I. Therefore, AO is the real depth and IO is the apparent depth of that object.

From Snell’s law,
aµw = sin r / sin i     (where i is the angle of incident, and r is the angle of refraction)
 
In ΔABO, sin I = AB / OB
And in ΔABI, sin r = AB / IB
Then, aµw = sin i / sin r
                = (AB/IB) / (AB/OB)                                                                                      
                = OB/IB                                
 
If point B is very close to point A then                                                                                 
OB = OA and IB = IA so,
.: aµw= OA/IA = real depth/apparent depth ……(i)
 
Apparent Shift: if the real depth, OA = t, then from equation (i), apparent depth = t/aµw. The apparent shift of the object is given by
d = OI = OA – AI
          = Real depth – Apparent depth
          = t - t/aµw
  or, d = t (1 – 1/aµw)

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