228s12-l04

# 228s12-l04 - Physics 228 Today: Interference Website: Sakai...

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Physics 228 Today: Interference Website: Sakai 01:750:228 or www.physics.rutgers.edu/ugrad/228 We studied interference at some level in 124, so this should be largely review. Tuesday, February 21, 2012

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Inteference Why do we see the colors in the soap bubble? Interference. We will see how this works today. Tuesday, February 21, 2012
EM Waves First: recall the formula for a traveling plane wave of light, moving in the +z direction: ° E = E 0 cos( kz ωt x ° B = B 0 cos( kz ωt y Second: what happens when we have a point source emitting light uniformly in all directions? We get a spherical wave. The wave expands in r, not z, so the argument kz becomes kr. Energy conservation leads to the amplitude decreasing with r, since the area increases as r 2 . ° E ( r, t )= E 0 r cos( kr ωt ) ˆ θ ° B ( r, t )= B 0 r cos( kr ωt ) ˆ φ Tuesday, February 21, 2012

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Multiple Frequencies / Wavelengths The formula for a traveling spherical wave of light, moving in the +r direction: Note: implicit in these formulas we have a single frequency / wavelength of light. We will assume that to start, but we have to eventually think of having multiple frequencies / wavelengths of light at the same time. ° B ( r, t )= B 0 r cos( kr ωt ) ˆ φ ° E ( r, t )= E 0 r cos( kr ωt ) ˆ θ Tuesday, February 21, 2012
Spherical Wave The frst source emits light. The second source emits light ``in phase’’ with the frst source - ``peaks’’ and ``valleys’’ are emitted at the same time From each source. The waves are ``in phase’’ at points a and b, but not at point c. Tuesday, February 21, 2012

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Maxima and Minima At some places the waves add up and you get constructive interference and maxima.
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## 228s12-l04 - Physics 228 Today: Interference Website: Sakai...

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