Given that refractive index of soap is,
[tex]\mu=1.35[/tex]To obtain yellow light of wavelength
[tex]\lambda=580\text{ nm}[/tex]constructive interference is required.
The condition for it is
[tex]2\mu t=(n-\frac{1}{2})\lambda[/tex]Here, t is the thickness and n is any arbitrary number, whose value can be
n=1,2,3,.....
Substituting values for n=1
[tex]\begin{gathered} t1=\frac{(1-\frac{1}{2})580}{2\times1.35} \\ =107.4\text{ nm} \end{gathered}[/tex]Substituting values for n=2
[tex]\begin{gathered} t2=\frac{(2-\frac{1}{2})580}{2\times1.35} \\ =322.22\text{ nm} \end{gathered}[/tex]Substituting values for n=3
[tex]\begin{gathered} t3=\frac{(3-\frac{1}{2})580}{2\times1.35} \\ =\text{ 537.03 nm} \end{gathered}[/tex][tex]\begin{gathered} t3=\frac{(3-\frac{1}{2})580}{2\times1.35} \\ =\text{ 537.03 nm} \end{gathered}[/tex]