Question

Estimate the thickness of the polystyrene film that yielded the spectrum shown in Figure 16-1.

Short answer

The thickness of the film is $7.9\times {10}^{-3}\mathrm{cm}$.

Step-by-step solution

Step 1. Given information  

Determine the thickness of the polystyrene film.

Step 2. Explanation

The thickness of the polystyrene film is given as:
$b=\frac{\Delta N}{2\left({\overline{v}}_1-{\overline{v}}_2\right)}\dots \dots \text{(I)}$

Where,

$\Delta N:$Number of the interference fringes between the two wavelengths is ,

${\overline{v}}_1:$Wave number of the lower absorption bond is and

${\overline{v}}_2:$Wave number of the higher absorption bond.

Refer the fig 16-1

Get the number of the interference fringes between the two wavelengths as 12.64.

Wavenumber for the lower absorption bond as 2800 cm^-1and for the higher absorption bond as 2000 cm^-1.

Substitute these values in the equation, we get

$$\begin{gathered} b=\frac{12.64}{2\left(2800{\mathrm{cm}}^{-1}-2000{\mathrm{cm}}^{-1}\right)} \\ =\frac{12.64}{1600{\mathrm{cm}}^{-1}} \\ =7.9\times {10}^{-3}\mathrm{cm} \end{gathered}$$