W11Physics1CLec27Bfkw

# W11Physics1CLec27Bfkw - Physics 1C Lecture 27B Interference...

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Physics 1C Lecture 27B

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Interference in Thin Films Interference in soap bubbles. The colors are due to interference between light rays re±ected from the front and back surfaces of the thin ²lm of soap making the bubble. The color depends on the thickness of the ²lm. Black appears where the ²lm is thinnest. Red appears where the ²lm is thickest.
Interference in Thin Films With light incident on a thin ±lm we have to examine two light rays that follow the same path: Ray 1 (in air) re²ects off the ±lm surface and undergoes a phase change of 180 o compared to the incident ray. Ray 2 (in air) refracts at the ±lm surface and then re²ects off of Surface B (±lm to air) with no phase change compared to the incident wave.

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Interference in Thin Films In addition, Ray 2 travels a distance t down and and a distance t up (for a total distance 2 t ). Since the extra distance that Ray 2 travels is in the ±lm medium, its wavelength will be different then in air. The wavelength of light, λ n , in a medium with index of refraction n is: ! n = n where λ is wavelength of light in a vacuum (air?).
Interference in Thin Films In order for constructive interference to occur, the two rays must be in phase. This means that the difference in path length and phase must combine to m ( λ / n ) , where m = 0, ±1, ±2. .. The difference in path is: 2 t and the difference in phase is: Constructive Interference for 1 phase change. Combining all of these gives us: 1 2 ! ( ) 2 t ! 1 2 " n = m n 2 nt = m + 1 2 ( ) 180 o !

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Disclaimer We ignored the angle in this discussion. I.e. we assumed the light enters orthogonal to the surface of the Flm.
Diffraction Patterns The diffraction pattern appears on a screen when light passes through a narrow vertical slit. The pattern consists of a broad, intense central band and a series of less intense and narrower side bands. A diffraction pattern is just another interference pattern.

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Diffraction Patterns Diffraction pattern of a penny, taken with the penny midway between screen and source.
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## This note was uploaded on 01/30/2012 for the course PHYS 1C 1C taught by Professor Wethien during the Spring '11 term at UCSD.

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W11Physics1CLec27Bfkw - Physics 1C Lecture 27B Interference...

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