Question

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.

Answer 1

Given that refractive index of soap is,

`\mu=1.35`

To obtain yellow light of wavelength

`\lambda=580\text{ nm}`

constructive interference is required.

The condition for it is

`2\mu t=(n-(1)/(2))\lambda`

Here, t is the thickness and n is any arbitrary number, whose value can be

n=1,2,3,.....

Substituting values for n=1

`\begin{gathered} t1=((1-(1)/(2))580)/(2*1.35) \\ =107.4\text{ nm} \end{gathered}`

Substituting values for n=2

`\begin{gathered} t2=((2-(1)/(2))580)/(2*1.35) \\ =322.22\text{ nm} \end{gathered}`

Substituting values for n=3

`\begin{gathered} t3=((3-(1)/(2))580)/(2*1.35) \\ =\text{ 537.03 nm} \end{gathered}`
`\begin{gathered} t3=((3-(1)/(2))580)/(2*1.35) \\ =\text{ 537.03 nm} \end{gathered}`