week7 - Physics 1C Week 7 Interference of Light: Winter...

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1 Physics 1C Winter 2009 Class Notes Week 7 Walter Gekelman Interference of Light: If two vectors of equal magnitude and opposite direction are added their sum is zero. This is the basic principle of the interference of light. E = E 0 cos( kz ! " t ) ! E 0 cos( kz ! t ) = 0 . This is the electric field of two waves of light traveling in the same direction but the E field vector of one is pointing up and that of the other pointing down. This is also the same as saying there are two waves out of phase by 180 degrees: E = cos kz ! t ( ) + cos kz ! t + # ( ) if = $ then E = cos kz ! t ( ) ! cos kz ! t ( ) If we use our complex notation: ! E = E 0 e i kz ! t ( ) + E 0 e i kz ! t + ( ) = E 0 e i kz ! t ( ) + E 0 e i e i kz ! t ( ) , = e i = cos + i sin = ! 1 E = Re ! E = 0 Consider a source of monochromatic light, for example a laser. The light is expanded by lenses, to make a plane wave traveling in the x direction. The light then hits a screen with two narrow slits cut in it. The slits are aligned with the z axis and are very, very long. There is a photosensitive screen a distance L away from the slits. L is much larger than d, the distance between the slits. Each beam will travel a different distance to the screen. Let us write the relationship between the phase difference, which is important for interference, in terms of the path difference.
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2 (1) ! phase ( ) = ! " = 2 # $ ! path ( ) . This is because the path is going to be some number ( for example 320.7 ) wavelengths of the light. Each wavelength is a phase difference of 2 π . If the two beams combine in phase at a position on the wall you get a bright spot. If the beams are π out of phase they destructively interfere and you get darkness. This is illustrated in the figure below: We wish to make a plot of the intensity of light on the film for any position y on the wall. If we redraw the diagram for 2 rays of light: If d <<<L then the two lines S 1 P and S 2 P are nearly equal. (They are like the radius of a circle centered at P). This makes the difference in path between the rays dsin θ as shown.
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This note was uploaded on 01/21/2010 for the course PHYS 1C taught by Professor Whitten during the Winter '07 term at UCLA.

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week7 - Physics 1C Week 7 Interference of Light: Winter...

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