Calculate A film of oil (n=1.38) floats on a puddle of water...

Calculate A film of oil $(n=1.38)$ floats on a puddle of water $(n=1.33)$. You notice that green light $(\lambda=521 \mathrm{~nm})$ is absent in the reflection. What is the minimum thickness of the oil film?

Key Concepts

Interference Condition for Destructive Interference

For destructive interference in a thin film where one reflected ray undergoes a ? phase shift and the other does not, the condition is that the optical path difference plus the phase shift must equal an odd multiple of ?. This leads to the condition 2nd = (m + 1/2)?, where m is an integer (with the smallest nonzero thickness corresponding to m = 0) and ? is the wavelength of light in air. This condition is used to calculate the minimum film thickness required for the cancellation of a particular color.

Thin-Film Interference

Thin-film interference occurs when light reflects off different boundaries of a film whose thickness is comparable to the wavelength of light, causing multiple reflections that can interfere constructively or destructively. This phenomenon explains why films can show vibrant colors or, conversely, the absence of a specific color when conditions meet the criteria for destructive interference.

Phase Change Upon Reflection

When light reflects from a boundary between media, it may undergo a phase shift. In particular, reflection from a medium of higher refractive index results in a half-wavelength (or ? radian) phase shift, while reflection from a medium of lower refractive index does not. This phase change is crucial in determining the interference outcome between the waves reflecting off the different surfaces of the film.

Optical Path Difference

The optical path difference is the extra distance traveled by one of the waves, taking into account the refractive index of the film, compared to the other wave. In a thin film, this difference is typically given by 2nd (where n is the refractive index and d is the thickness of the film), and it directly influences the phase difference between the waves that interfere.

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