Question

a soap film (n = 1.33) reflects light, and the brightest color you see is blue light at 448 nm. if that is from the second longest (m = 2) possible wavelength, how thick is the soap film at that point?? nm

Explanation:

Step1: Recall thin film bright fringe formula

For constructive interference in a thin film with phase shifts at both surfaces (air-soap and soap-air, since $n_{\text{air}} < n_{\text{soap}}$), the formula is:
$$2nt = m\lambda$$
where $n$ = refractive index, $t$ = film thickness, $m$ = order, $\lambda$ = wavelength in vacuum.

Step2: Rearrange for thickness $t$

Isolate $t$ by dividing both sides by $2n$:
$$t = \frac{m\lambda}{2n}$$

Step3: Substitute given values

$m=2$, $\lambda=448$ nm, $n=1.33$:
$$t = \frac{2 \times 448}{2 \times 1.33} = \frac{448}{1.33} \approx 209 \text{ nm}$$

Answer:

209 nm