Question

at a particular spot on an oil film on top of water (n = 1.42), you see green light at 500 nm. if that is from the second longest (m = 2) possible wavelength, how thick is the oil spot at that point? ? nm

Explanation:

Step1: Recall thin film interference formula

For constructive interference in a thin film (oil on water, with phase shifts at both top and bottom surfaces leading to net zero phase difference shift for the reflected light), the formula is:
$$2nt = m\lambda$$
where $n=1.42$ (refractive index of oil), $t$ is film thickness, $m=2$ (order of the wavelength), $\lambda=500\ \text{nm}$ (wavelength in vacuum).

Step2: Rearrange for thickness $t$

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

Step3: Substitute values and calculate

Plug in $m=2$, $\lambda=500\ \text{nm}$, $n=1.42$:
$$t = \frac{2 \times 500}{2 \times 1.42} = \frac{500}{1.42} \approx 423\ \text{nm}$$

Answer:

423 nm