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An ink mark is made on a piece of paper on which a glass slab of thickness ' $t$ ' is placed. The ink mark appears to be raised up through a distance ' $x$ ' when viewed at nearly normal incidence. If the refractive index of the material of glass slab is ' $\mu$ ' then the thickness of glass slab is given by
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Verified Answer
The correct answer is:
$\frac{\mu \mathrm{x}}{\mu-1}$
Here, the normal shift is $\mathrm{x}$ The formula for the normal shift is
$$
\begin{aligned}
x & =t\left(1-\frac{1}{\mu}\right) \\
t & =\frac{x}{\left(1-\frac{1}{\mu}\right)} \\
x & =t\left(1-\frac{1}{\mu}\right) \\
t & =\frac{x}{\left(1-\frac{1}{\mu}\right)} \\
\therefore \quad t & =\frac{x \mu}{(\mu-1)}
\end{aligned}
$$
$$
\begin{aligned}
x & =t\left(1-\frac{1}{\mu}\right) \\
t & =\frac{x}{\left(1-\frac{1}{\mu}\right)} \\
x & =t\left(1-\frac{1}{\mu}\right) \\
t & =\frac{x}{\left(1-\frac{1}{\mu}\right)} \\
\therefore \quad t & =\frac{x \mu}{(\mu-1)}
\end{aligned}
$$
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