A film of oil on water will appear dark when it is very thin, because thepath length difference becomes small compared with the wavelength oflight and there is a phase shift at the top surface. If it becomes dark whenthe path length difference is less than one-fourth the wavelength, what isthe thickest the oil can be and appear dark at all visible wavelengths? Oilhas an index of refraction of 1.40. Take 380 nm to be the shortest visiblewavelength in air.

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