91Ó°ÊÓ

Monochromatic lights are single-wavelength light, where mono refers to single, and chrome means color. Visible light of a narrow band of wavelengths is classified as monochromatic lights. It features a wavelength within a short wavelength range.

The expression for the minima condition for normal incidence in the case of thin films is,

$2L=m\frac{\mathrm{λ}}{n}$

Here, L is thickness, m is order, $\mathrm{λ}$ is wavelength, and n is refractive index of medium.

In case of 4001 dark fringe with index of right in air $n_{air}$, the condition of minima

$2L=\left(4001\right)\frac{\mathrm{λ}}{n_{air}}$

In the case of 4000 dark fringe with index c vacuum 1.0 the condition for minima:

$2L=\left(4000\right)\frac{\mathrm{λ}}{1.0}$

For both conditions the left side of the equation is 2L.

Thus the equation right hand side and solve for $n_{air}$.

$\begin{array}{rcl}\left(4001\right)\frac{\mathrm{λ}}{n_{air}}& =& \left(4000\right)\frac{\mathrm{λ}}{1.0}\\ n_{air}& =& 1.00025\end{array}$

Hence, the refractive index of air is $1.00025$.