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Homework Help: Find Apparent depth due to a non-homogenous liquid

  1. Mar 22, 2012 #1

    A vessel of depth H is filled with a non-homogenous liquid whose refractive index varies with y as u=(2 -(y/H)), where y is measured from bottom of the vessel. Find the apparent depth as seen by an observer from above?
    (Paraxial approximation is allowed)


    We know in paraxial approximation


    Where u1 is refractive index of medium 1, x is object distance from surface, u2 is refractive index of surrounding medium , y2 is apparent depth.


    I took a differential strip of thickness dy at a height of y from bottom.
    its refractive index is
    (2-(y/H)-(dy/H)) and refractive index of element just below it is (2-(y/H))

    Lets say that the image of the bottom of the vessel formed by refraction from all strips below this height y be at a distance x from the bottom.

    Therefore, Its distance from the strip is y-x.

    So using the formulae i mentioned.


    So ydx/H -2dx=-ydy/H+xdy/H.

    After this am struck cause I cannot integrate.

    I know other ways of solving this problem(mentioned in my text book), but I wanna know what exactly am I doing wrong here?
    Any help/inputs will be really appreciated.
  2. jcsd
  3. Mar 22, 2012 #2
    Never mind.I figured it out :-)

    Admin can delete the thread
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