Lecture 19 (Ch. 27.1-27.3)

# Lecture 19 (Ch. 27.1-27.3) - Lecture 19 Wave Optics Ch 27...

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Lecture 19 Wave Optics Ch 27

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Wave Optics o Recall that the ray model is valid (light travels in straight lines) only if the light does not encounter structures comparable in size to the wavelength o In other cases, we must account for the wave-like behavior of light [WAVE OPTICS]
Interference of Light o Like all waves, light obeys the superposition principle and can exhibit interference The intensity of a light wave is related to the square of the oscillating E and B vectors o When light interferes, we add the field vectors to get the net amplitude and then square that sum to get the intensity Light intensity (like the power of a mechanical wave) is proportional to the square of the amplitude o Just like in sound waves, light waves must be coherent (in phase) in order to interfere. Obtaining a constant phase relationship with light sources usually requires passing a single light source through two narrow slits…more on that later.

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Phase Difference and Interference o Remember the relationship for the phase difference ( Δφ ) that we used for sound: Δφ / (2 π ) = Δ r / λ o A phase difference of 0 (or 2 π , 4 π , etc) corresponds to constructive interference o A phase difference of π (or 3 π , 5 π , etc) corresponds to destructive interference
Young’s Double-Slit Experiment o Classic 1801 experiment seemed to prove once and for all that light is a wave o A single slit in the first barrier is used to produce light, which then meets a second barrier with two slits o Due to interference between light from the two slits, a pattern of light and dark regions is produced on a screen

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Two Slits vs. Two Speakers o The two-slit experiment (with light) is very similar to the case of two speakers (with sound). Each slit (S 1 or S 2 ) corresponds to a speaker driven in phase o As before there are nodes (places with destructive interference - minima) and anti-nodes (constructive interference - maxima)
Interference Fringes o The light and dark regions are called “fringes” o Bright regions are constructive interference. o Dark regions are destructive interference.

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Constructive & Destructive Interference The two waves leave the source in phase, and strike the point P after traveling EQUAL distances => Δφ =0 no phase difference => bright spot. Waves from source S1 travel exactly 1 wavelength further than those from source S2 => Δφ = 2 π constructive interference => bright spot.
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