logistic_guy
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If a soap bubble is \(\displaystyle 120 \ \text{nm}\) thick, what color will appear at the center when illuminated normally by while light? Assume that \(\displaystyle n = 1.34\).
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logistic_guy
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White light means that we have a mix of visible light waves in air. Usually those waves to be seen by the eye, their length lies in the interval:
\(\displaystyle 400 \ \text{nm} \leq \lambda \leq 700 \ \text{nm}\)
We use the wavelength in air formula to solve this problem.
\(\displaystyle \lambda = \frac{2tn}{m + \frac{1}{2}}\)
where \(\displaystyle m = 0,1,2,\cdots\) are interference orders (or fringe orders).
Let us try \(\displaystyle m = 0\).
\(\displaystyle \lambda_0 = \frac{2(120 \ \text{nm})(1.34)}{0 + \frac{1}{2}} = 643.2 \ \text{nm}\)
Let us try \(\displaystyle m = 1\).
\(\displaystyle \lambda_1 = \frac{2(120 \ \text{nm})(1.34)}{0 + \frac{1}{2}} = 214.4 \ \text{nm}\)
No need to check more values because the wavelengths are getting much smaller. Therefore, the only visible wave has the wavelength:
\(\displaystyle \lambda = \textcolor{blue}{643.2 \ \text{nm}}\)
This wavelength lies in the \(\displaystyle \textcolor{red}{\text{red}}\) color spectrum but it is very close to the \(\displaystyle \textcolor{orange}{\text{orange}}\) color spectrum.
Therefore, for safety, it is better to say that the color that will appear at the center is \(\displaystyle \textcolor{blue}{\text{orange-red}}\).
\(\displaystyle 400 \ \text{nm} \leq \lambda \leq 700 \ \text{nm}\)
We use the wavelength in air formula to solve this problem.
\(\displaystyle \lambda = \frac{2tn}{m + \frac{1}{2}}\)
where \(\displaystyle m = 0,1,2,\cdots\) are interference orders (or fringe orders).
Let us try \(\displaystyle m = 0\).
\(\displaystyle \lambda_0 = \frac{2(120 \ \text{nm})(1.34)}{0 + \frac{1}{2}} = 643.2 \ \text{nm}\)
Let us try \(\displaystyle m = 1\).
\(\displaystyle \lambda_1 = \frac{2(120 \ \text{nm})(1.34)}{0 + \frac{1}{2}} = 214.4 \ \text{nm}\)
No need to check more values because the wavelengths are getting much smaller. Therefore, the only visible wave has the wavelength:
\(\displaystyle \lambda = \textcolor{blue}{643.2 \ \text{nm}}\)
This wavelength lies in the \(\displaystyle \textcolor{red}{\text{red}}\) color spectrum but it is very close to the \(\displaystyle \textcolor{orange}{\text{orange}}\) color spectrum.
Therefore, for safety, it is better to say that the color that will appear at the center is \(\displaystyle \textcolor{blue}{\text{orange-red}}\).