A particular kind of oil with an index of refraction of $1.46$ has spilled on water. The different thicknesses of the oil slick result in different colors being strongly reflected at different parts of the spill. But near the edges, you identify the thinnest part of the oil layer that strongly reflects green light with a wavelength of 550 nm when you are directly overhead. What is the thickness of the oil at this point? Assume light is incident normal to the oil surface.

• A. $103\mathrm{nm}$
• B. $138\mathrm{nm}$
• C. $188\mathrm{nm}$
• D. $275\mathrm{nm}$
• E. $377\mathrm{nm}$
• F. $94.2\mathrm{nm}$

Answer: (F)

Verified step by step guidance

1. Understand that the problem involves thin film interference, where light reflects off the top and bottom surfaces of the oil layer, causing constructive or destructive interference.
2. Recognize that for constructive interference, the path difference between the two reflected rays must be an integer multiple of the wavelength in the medium. The formula for constructive interference in thin films is: 2 * t * n = m * λ, where t is the thickness of the film, n is the refractive index, m is the order of interference, and λ is the wavelength of light in vacuum.
3. Convert the wavelength of green light from vacuum to the medium (oil) using the formula: λ_medium = λ_vacuum / n. Here, λ_vacuum is 550 nm and n is 1.46.
4. Substitute the values into the formula for constructive interference to solve for the thickness t. You will need to consider the smallest non-zero integer m that results in constructive interference.
5. Evaluate the possible thickness values given in the problem and determine which one corresponds to the calculated thickness for the first order of constructive interference (m = 1).