91Ó°ÊÓ

Bright colors reflected from thin oil on water and soap bubbles are a consequence of light interference. Due to the constructive interference of light reflected from the front and back surfaces of the thin film, these bright colors can be seen. For a perpendicular incident beam, the maximum intensity of light from the thin film satisfies the condition:

$\mathbf{2}\mathbf{L}\mathbf{=}\left(m+\frac{1}{2}\right)\frac{\mathbf{λ}}{{\mathbf{n}}_{\mathbf{2}}}\mathbf{\text{ â¶Ä‰â¶Ä‰}}\mathbf{m}\mathbf{=}\mathbf{0}\mathbf{,}\mathbf{\text{ }}\mathbf{1}\mathbf{,}\mathbf{\text{ }}\mathbf{2}\mathbf{,}\mathbf{.}\mathbf{..}$(Maxima—bright film in the air)

where λ is the wavelength of the light in air, L is its thickness, and n₂ is the film’s refraction index.

The least and the 2^nd least thickness are associated with $\text{m}=0,\text{ }1$the order of maximum intensity. The thickness corresponding to this order of maxima is

For $\text{m}=0$;

$\begin{array}{c}{\mathrm{L}}_{\mathrm{o}}=\left(\mathrm{m}+\frac{1}{2}\right)\frac{\mathrm{λ}}{2{\mathrm{n}}_2}\\ =\left(0+\frac{1}{2}\right)\frac{624\text{ }\mathrm{nm}}{2\left(1.33\right)}\\ =117\text{ }\mathrm{nm}\end{array}$

For $\text{m}=1$;

$\begin{array}{c}{\mathrm{L}}_1=\left(\mathrm{m}+\frac{1}{2}\right)\frac{\mathrm{λ}}{2{\mathrm{n}}_2}\\ =\left(1+\frac{1}{2}\right)\frac{624\text{ }\mathrm{nm}}{2\left(1.33\right)}\\ =352\text{ }\mathrm{nm}\end{array}$

Thus, the least thickness is 117 nm, and the 2^nd least thickness is 352 nm.