A student looking straight on the soap film observes it being yellow. Assuming the wavelength of the yellow light is 580. nm compute 3 possible values for the thickness of the soap film. The index of refraction for the soap is 1.35.

Respuesta :

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]