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An oil film (n = 1.42) floating on water is 264 nm thick. What is the second longest (m = 2) wavelength IN NANOMETERS that reflects brightlyfrom the film?(Hint: If you leave the wavelength in nm, the answer will be in nm. No conversion necessary.)(Unit = nm)

Answer :

ANSWER

[tex]500\text{ nm}[/tex]

EXPLANATION

To find the second longest wavelength that reflects brightly from the film, apply the expression for constructive interference:

[tex]2nt+\frac{\lambda}{2}=m\lambda[/tex]

where m = 2

n = refractive index

λ = wavelength

Make λ the subject of the formula:

[tex]\begin{gathered} 2nt=mλ-\frac{λ}{2} \\ \\ 2nt=(2m-1)\frac{λ}{2} \\ \\ \frac{λ}{2}=\frac{2nt}{2m-1} \\ \\ λ=\frac{4nt}{2m-1} \end{gathered}[/tex]

Now, calculate the wavelength by substituting the given values into the equation:

[tex]\begin{gathered} λ=\frac{4*1.42*264}{2(2)-1} \\ \\ λ=\frac{1499.52}{4-1}=\frac{1499.52}{3} \\ \\ λ=499.84\text{ nm}\approx500\text{ nm} \end{gathered}[/tex]

That is the answer.

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