Question

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 1

`500\text{ nm}`

Step-by-step explanation

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

`2nt+(\lambda)/(2)=m\lambda`

where m = 2

n = refractive index

λ = wavelength

Make λ the subject of the formula:

`\begin{gathered} 2nt=mλ-(λ)/(2) \\ \\ 2nt=(2m-1)(λ)/(2) \\ \\ (λ)/(2)=(2nt)/(2m-1) \\ \\ λ=(4nt)/(2m-1) \end{gathered}`

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

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

That is the answer.