Question

The difference in the number of wavelengths, when yellow light propagates through air and vaccum columns of the same thickness is one.The thickness of the column is $x\text{mm}$. The value of $x$ is
[Refractive index of air ${\mu }_{air}=1.0003$, wavelength of yellow light in vaccum $=6000\mathring{A}$].

Answer 1

Difference in number of wavelength is given as one
Let $t$ be the thickness of the column.
So, $\frac{t}{{\lambda }_{air}}-\frac{t}{{\lambda }_{vaccum}}=1$
$t(\frac{1}{{\lambda }_{air}}-\frac{1}{{\lambda }_{vaccum}})=1$
$\frac{t}{{\lambda }_{vaccum}}({\mu }_{air}-1)=1$
$\Rightarrow t=\frac{{\lambda }_{vaccum}}{({\mu }_{air}-1)}=\frac{6\times {10}^{-7}}{(1.0003-1)}=2\text{mm}$
Hence, the value of $x$ is $2$.