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A printed page is kept pressed by a transparent cube of edge t. The refractive index of the cube varies us mu (z) =1 + z /t, where x is the vertical distance from bottom of the cube. If viewed from top, then the printed letters appear to be shifted by an amount |
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Answer» `(1-ln2) t `  Condider an ELEMENTAL strip at a height z of thickness dz. Apparent height =`("Real height ")/(RI)= (d)/(mu(z))` `dh = (dz)/(1+ (z)/(t))` `dh = ((t)/(t +z))dz` `h INT _(0) ^(z) (t)/(t +z).dz` `h = [t ln (t + z) ]_(0)^(2) =t [ln (1+ t) - ln (t+ 0)]` `h = t ln ""(2t)/(t) = t ln 2` Shift, `Deltax, = t- t ln2` `implies Delta X = (1- ln 2) t ` |
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