Question

at a particular spot on an oil film on top of water (n = 1.42), the brightest color you see is blue light at 482 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 interference formula

For constructive interference in a thin film where the film has a higher refractive index than the surrounding medium (air, \(n \approx 1\)) and the lower medium (water, \(n=1.33 < 1.42\)), there is a single phase shift, so the formula is:
$$2nt = m\lambda$$
where \(n\) = refractive index of oil, \(t\) = film thickness, \(m\) = order of interference, \(\lambda\) = wavelength of light in vacuum.

Step2: Rearrange for thickness \(t\)

Isolate \(t\) from the formula:
$$t = \frac{m\lambda}{2n}$$

Step3: Substitute given values

\(m=1\), \(\lambda=482\ \text{nm}\), \(n=1.42\):
$$t = \frac{1 \times 482}{2 \times 1.42} = \frac{482}{2.84} \approx 84.6\ \text{nm}$$

Answer:

84.6 nm