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A printed page is pressed by a glass of water. The refractive index of the glass and water is 1.5 and 1.33, respectively, if the thickness of the bottom of glass is 1 cm and depth of water is 5 cm how much the page will appear to be shifted if viewed from the top?

Last updated date: 29th Feb 2024
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Hint: In this question we will use the relation between the apparent depth and refractive index of the medium. Further, we will use this value to find the shift. We will also discuss the basics of apparent depth and real depth for better understanding.
Formula used:
$h' = \dfrac{{{h_1}}}{{\mu {}_1}} + \dfrac{{{h_2}}}{{{\mu _2}}}$
$\Delta h = h - h'$

As we know that the apparent depth in a medium is defined as the depth of an object in a denser medium when seen from the rarer medium. The value of apparent depth is smaller than the real depth.
As we know, the apparent depth is given by:
$h' = \dfrac{{{h_1}}}{{\mu {}_1}} + \dfrac{{{h_2}}}{{{\mu _2}}}$
$\Rightarrow h' = \dfrac{1}{{1.5}} + \dfrac{5}{{1.33}} = 4.43cm$
From the above equation we can calculate normal shift as:
$\Delta h = h - h'$
\eqalign{& \Rightarrow \Delta h = 6 - 4.43 \cr & \therefore \Delta h = 1.57cm \cr}
Therefore, from the above result we can say that the page will appear to be shifted 1.57cm if viewed from the top.