A film of gasoline (n=1.40) floats on water (n=1.33). Normally incident blue light of a wavelength 480 nm, appears bright blue due to constructive interference. Determine the minimum non-zero thickness of the film
Please Help, I've been stuck in this question for two days :-(
To determine the minimum non-zero thickness of the film that produces the observed bright blue color due to constructive interference, we can use the thin film interference formula:
2nt = mλ
where:
- t is the thickness of the film (in meters)
- n is the refractive index of the film
- m is the order of the interference (m = 0, 1, 2, ...)
- λ is the wavelength of the light (in meters)
First, we need to convert the given wavelength from nm to meters:
λ = 480 nm = 480 × 10^(-9) m
Using the given refractive index for gasoline (n = 1.40) and water (n = 1.33), we can substitute these values into the formula:
2nt = mλ
For constructive interference (bright blue color), we are interested in the first order of interference (m = 1). Rearranging the formula, we can solve for the thickness t:
t = (mλ) / (2n)
Substituting the values:
t = (1 × 480 × 10^(-9) m) / (2 × 1.40)
t ≈ 0.171 × 10^(-6) m
Therefore, the minimum non-zero thickness of the film that produces the observed bright blue color is approximately 0.171 × 10^(-6) meters.