Question

at a particular spot on an oil film on top of water (n = 1.41), the brightest color you see is red light at 650 nm. if that is from the longest (m = 1) wavelength possible, how thick is the oil spot at that point? ? nm

Explanation:

Step1: Recall thin film bright fringe formula

For constructive interference in a thin film where the film has a higher refractive index than the surrounding medium (air, \(n=1\)) and the substrate (water, \(n\approx1.33 < 1.41\)), the path difference condition is \(2nt = m\lambda\), where \(n\) is the film refractive index, \(t\) is film thickness, \(m\) is the order, and \(\lambda\) is the wavelength in vacuum.

Step2: Rearrange formula to solve for \(t\)

\(t = \frac{m\lambda}{2n}\)

Step3: Substitute given values

\(m=1\), \(\lambda=650\ \text{nm}\), \(n=1.41\)
\(t = \frac{1\times650}{2\times1.41} = \frac{650}{2.82} \approx 182\ \text{nm}\)

Answer:

182 nm