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Why is it the wavelength in the film itself that matters

Why is it the wavelength in the film itself that matters -...

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Why is it the wavelength in the film itself that matters? The light reflecting off the top surface of the film does not pass through the film at all, so how can it be the wavelength in the film that is important in thin-film interference? A diagram can help clarify this. The diagram looks a little complicated at first glance, but it really is straightforward once you understand what it shows. Figure A shows a wave incident on a thin film. Each half wavelength has been numbered, so we can keep track of it. Note that the thickness of the film is exactly half the wavelength of the wave when it is in the film. Figure B shows the situation two periods later, after two complete wavelengths have encountered the film. Part of the wave is reflected off the top surface of the film; note that this reflected wave is flipped by 180°, so peaks are now troughs and troughs are now peaks. This is because the wave is reflecting off a higher-n medium.
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