A thin film of oil (n=1.35) floats on a puddle of water...

A thin film of oil $(n=1.35)$ floats on a puddle of water $(n=1.33)$. If light with a wavelength of $590 \mathrm{~nm}$ experiences destructive interference when it reflects from the film, what is the minimum thickness of the oil?

Key Concepts

Phase Change upon Reflection

When light reflects at an interface between two media, the phase of the reflected light may change. Specifically, if light reflects off a medium with a higher refractive index than the incident medium, it undergoes a half-wavelength (? radians) phase shift. No phase shift occurs when reflecting from a medium of lower refractive index. This difference is essential for calculating the net phase difference in thin film interference.

Interference Condition for Destructive Interference

For destructive interference in thin films, the condition is that the total phase difference—including both the phase shift from the optical path and any reflection phase changes—results in the two reflected waves being out of phase. When one reflection undergoes a half-wavelength shift and the other does not, the simplest condition for minimal reflection (complete destructive interference) becomes 2n·t = m? (with m being a positive integer and the smallest non?zero thickness corresponding to m = 1), thereby setting the film thickness needed for cancellation of the reflected waves.

Thin Film Interference

Thin film interference occurs when light waves reflected from both the top and bottom surfaces of a film combine. The interference pattern—whether constructive (bright) or destructive (dark)—depends on the phase difference between these waves, which arises from both the optical path difference inside the film and any phase shifts upon reflection at the interfaces.

Optical Path Length

Optical path length is the product of the physical thickness of the film and the refractive index of the material. It represents the effective distance traveled by light in a medium as compared to its travel in a vacuum. This concept is critical in determining the phase difference between light rays within the film.

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