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

Answer:

85.2 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 \approx 1)) and the lower medium (water, (n=1.33 < 1.42)), there is a single phase shift, so the formula is: $$2nt = m\lambda$$

Step2: Rearrange for film thickness (t)

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

Step3: Substitute given values

Use (m=1), (\lambda=482\ \text{nm}), (n=1.42): $$t = \frac{1 \times 482}{2 \times 1.42} = \frac{482}{2.84} \approx 85.2\ \text{nm}$$