91Ó°ÊÓ

• The width of the thin film increases downward.
• The film is illuminated with a beam of red light.

The expression to calculate the wavelength inside the film is given as follows.

$\mathit{L}\mathbf{=}\mathit{m}\frac{\mathbf{λ}}{\mathbf{2}\mathbf{n}}$

Here, n is the refractive index of the medium, $\mathit{λ}$is the wavelength, L is the thickness of the firm, and m is the order of the interference and it can take values 0,1,2,3........

The bright fringes in the thin films produce when 2L is equal to multiple of wavelength.

$2L=m{\mathrm{λ}}_t$

Substitute$\frac{\mathrm{λ}}{n}$for${\mathrm{λ}}_t$into above equation.

$$\begin{gathered} 2L=m\frac{\mathrm{λ}}{n} \\ L=m\frac{\mathrm{λ}}{2n} \end{gathered}$$

............(i)

Between points, a and b, the order of the interference is 1. Therefore,

m=1

Substitute 1 for m into equation (i).

$$\begin{gathered} L=\left(1\right)\frac{\mathrm{λ}}{2n} \\ L=\frac{\mathrm{λ}}{2n} \end{gathered}$$

Hence, the difference in the thickness between points a and b is$\frac{\mathrm{λ}}{2a}$.

Since between points b and d, the order of the interference is 2. Therefore,

m=2

Substitute 2 for m into equation (i)

$\begin{array}{rcl}L& =& \left(2\right)\frac{\mathrm{λ}}{2n}\\ L& =& \frac{\mathrm{λ}}{n}\\ & & \end{array}$