A thin film of oil (n=1.50) is spread over a puddle of water...

A thin film of oil $(n=1.50)$ is spread over a puddle of water $(n=1.33)$. In a region where the film looks red from directly above $(\lambda=630 \mathrm{~nm})$, what is the minimum possible thickness of the film?

Key Concepts

Thin Film Interference

Thin film interference is a phenomenon where light waves reflected from the top and bottom surfaces of a thin film interfere with one another. This interference can lead to enhancement or cancellation of certain wavelengths, resulting in the appearance of vivid colors. The effect depends on the film's thickness, the refractive indices of the materials involved, and the wavelength of the incident light.

Optical Path Difference (OPD)

The optical path difference is the extra distance a light wave travels in one medium compared to another, adjusted by the medium’s refractive index. In thin film interference, the OPD arises due to the difference in physical path lengths taken by light reflecting off the top and bottom surfaces of the film, and it plays a critical role in determining the phase difference between the waves.

Phase Change Upon Reflection

When light reflects at the boundary between two media, it may undergo a phase shift depending on the refractive indices of the materials. Specifically, a phase change of ? (or half a wavelength) occurs when light reflects off a medium with a higher refractive index than the one it is coming from. This phase shift must be accounted for when determining the conditions for constructive or destructive interference in thin films.

Constructive Interference Conditions

Constructive interference occurs when the reflected light waves are in phase, meaning their peaks align to enhance the resultant intensity. In thin film interference, this condition is achieved when the optical path difference—taking into account both the physical path length differences and any phase shifts upon reflection—is equal to an integer multiple of the wavelength (or, after adjusting for a half-wavelength phase shift, a half-integral multiple of the wavelength). This principle is used to determine the thickness of the film that reinforces the observation of specific colors.

Refractive Index and Wavelength Relation

The refractive index of a medium affects the speed of light and consequently the wavelength of light within that medium. The wavelength in the medium is given by the vacuum wavelength divided by the refractive index. This adjustment is essential in calculating the optical path length and understanding how the physical thickness of a film correlates with the interference patterns observed.

Please give Ace some feedback