An ink mark is made on a piece of paper on which a glass slab of thickness ' $t$ ' is placed. The ink mark…
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
$\frac{\mu \mathrm{x}}{\mu-1}$
$\frac{(\mu-1)}{\mu}$
$\frac{\mu-1}{\mu \mathrm{x}}$
$\frac{\mu}{(\mu-1) x}$
Solution
Here, the normal shift is $\mathrm{x}$ The formula for the normal shift is
$\begin{aligned}
x & =t\left(1-\frac{1}{\mu}\right) \\
t & =\frac{x}{\left(1-\frac{1}{\mu}\right)} \\
x & =t\left(1-\frac{1}{\mu}\right) \\
t & =\frac{x}{\left(1-\frac{1}{\mu}\right)} \\
\therefore \quad t & =\frac{x \mu}{(\mu-1)}
\end{aligned}$