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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 $1 \mathrm{~cm}$ and depth of water is $5 \mathrm{~cm}$, how much the page will appear to be shifted if viewed from the top ?
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The correct answer is:
$1.3533 \mathrm{~cm}$
$1.3533 \mathrm{~cm}$
Real depth $=5 \mathrm{~cm}+1 \mathrm{~cm}=6 \mathrm{~cm}$
Apparent depth $=\frac{\mathrm{d}_1}{\mu_1}+\frac{\mathrm{d}_2}{\mu_2}+\ldots$
$=\frac{5}{1.33}+\frac{1}{1.5}$
$\simeq 3.8+0.7 \simeq 4.5 \mathrm{~cm}$
$\therefore$ Shift $=6 \mathrm{~cm}-4.5 \mathrm{~cm} \cong 1.5 \mathrm{~cm}$
Apparent depth $=\frac{\mathrm{d}_1}{\mu_1}+\frac{\mathrm{d}_2}{\mu_2}+\ldots$
$=\frac{5}{1.33}+\frac{1}{1.5}$
$\simeq 3.8+0.7 \simeq 4.5 \mathrm{~cm}$
$\therefore$ Shift $=6 \mathrm{~cm}-4.5 \mathrm{~cm} \cong 1.5 \mathrm{~cm}$
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