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Chapter 32: Problem 70

You're investigating an oil spill for your state environmental protection agency. There's a thin film of oil on water, and you know its refractive index is \(n_{\text {oil }}=1.38 .\) You shine white light vertically on the oil, and use a spectrometer to determine that the most strongly reflected wavelength is \(580 \mathrm{nm}\). Assuming first-order thin-film interference, what do you report for the thickness of the oil slick?

Short Answer

Expert verified
The thickness of the oil slick is approximately \(2.10 \times 10^{-7}\)m.

Step by step solution

01

Identifying the relevant information

The first step involves identifying all the necessary information from the problem statement. We are given that the order of interference \(m\) equals 1 (it is first-order interference), the refractive index \(n_{\text{oil}}\) is 1.38, and the wavelength of the light \(\lambda\) is \(580nm = 580 \times 10^{-9}\)m.
02

Plugging in the values in the formula

The second step is inputting these values into the thin-film interference formula \(2nt=m\lambda\) in order to solve for \(t\), the thickness of the oil film. So this gives us the equation \(2t \times 1.38 = 1 \times 580 \times 10^{-9}\)m.
03

Solving for the thickness of the oil slick

Lastly, solve the equation for \(t\). Dividing both sides by \(2 \times 1.38\), we find that \(t = \frac{580 \times 10^{-9}\text{m}}{2 \times 1.38}\)

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