Question

At a particular spot on a soap bubble (n = 1.33), you see yellow light at 575 nm. If that is from the second longest (m = 2) possible wavelength, how thick is the bubble at that point IN NANOMETERS?(Hint: If you leave the wavelength in nm, the answer will be in nm. No conversion necessary.)(Unit = nm)

Answer 1

`\begin{equation*} 324.25\text{ nm} \end{equation*}`

Step-by-step explanation

To find the thickness of the bubble at that point, apply the condition for constructive interference:

`2nd\cos\theta=(2m+1)(\lambda)/(2)`

where d = thickness

n = refractive index

m = 0, 1, 2...

For the second longest wavelength, m = 1, and for normal incidence:

`\theta=0\degree`

Therefore, substituting the given values into the equation and solving for d:

`\begin{gathered} 2nd\cos0=(3)/(2)\lambda \\ \\ 2nd=(3)/(2)\lambda \\ \\ d=(3\lambda)/(4n)=(3*575)/(4*1.33) \\ \\ d=324.25\text{ nm} \end{gathered}`

That is the thickness of the bubble.