   Chapter 27, Problem 78PE

Chapter
Section
Textbook Problem

A film of oil on water will appear dark when it is very thin, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the oil can be and appear dark at all visible wavelengths? Oil has an index of refraction of 1.40.

To determine

Thickness of the oil film

Explanation

Given info:

Refractive index of oil, n=1.40

Formula used:

Thickness of the film producing destructive interference is calculated by the formula

2t=λ4n

Here,

λ is the wavelength of the reflected light

n is the refractive index

t is the thickness of the film producing interference

Calculation:

The visible spectrum comes in the range of 400nm-700nm now for destructive interference pattern for all the visible light spectrum, minimum wavelength of the light spectrum should be used

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