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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 :

ANSWER

[tex]\begin{equation*} 324.25\text{ nm} \end{equation*}[/tex]

EXPLANATION

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

[tex]2nd\cos\theta=(2m+1)\frac{\lambda}{2}[/tex]

where d = thickness

n = refractive index

m = 0, 1, 2...

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

[tex]\theta=0\degree[/tex]

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

[tex]\begin{gathered} 2nd\cos0=\frac{3}{2}\lambda \\ \\ 2nd=\frac{3}{2}\lambda \\ \\ d=\frac{3\lambda}{4n}=\frac{3*575}{4*1.33} \\ \\ d=324.25\text{ nm} \end{gathered}[/tex]

That is the thickness of the bubble.

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