How does interference occur in thin films?
Why is it important that the films be thin? Why don’t you get these effects with a relatively thick film? Where should you put the dividing line between "thin" and "thick"? Explain your reasoning.
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Thin film interference exists when the thickness of the coating is approximately the same as a multiple of a quarter wavelength of light. Reflections of light can be made to add destructively by choosing a film thickness that is one-quarter of a wavelength. A quarter wavelength is choosen because a wave reflected from the second boundary traverses the length of the coating twice-- forward, and then backward. Hence, when returns to the first boundary, it is one-half of a wavelength (180 degrees) out of phase with the reflection from the first boundary. Thus the reflected light, which is much weaker than the transmitted/incident light, is canceled out. Note that thin film interference is very dependant on the incident angle of the light, since light at oblique angles will travel farther within the thin film, and exit the coating at a different point than where it entered. Both these factors introduce a phase-shift-error relative to the quarter-wave matching criterion.
Note that the interference of the two reflections (one at the top of the coating and one from the bottom of the coating) results in a wave with zero amplitude only if the intensities of the two waves are equal. Thus, destructive interference will only occur if a) the second reflection is not attenuated in the coating material and b) slight deviations from normal incidence do not result in severe phase-shift errors. It is this latter restriction that limits the thickness of an anti-reflection coating in most instances. Typically, this limits the thickness of the film to less than that of a wavelength. Hence, the response to your criteria defining the boundary between "thick" and "thin" films is likely whether they are thicker than the wavelength of the light, typically near quarter-wavelength thickness.
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