Lecture 2

# Lecture 2 - Diffraction Lecture 4 Diffraction Reading Ch 36...

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1 Diffraction Diffraction Lecture 4: Diffraction Reading: Ch. 36 Main Idea: Diffraction is a behavior that belongs exclusively to waves: EM, mechanical, and matter waves. Traveling waves passing through an aperture spread out forming a recognizable pattern that can be used as an important analysis tool.

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2 Diffraction of Waves Diffraction of Waves Unique property of all waves: mechanical, EM, and matter → sound bends around corners, shadows are “fuzzy” and not sharp Waves “flare out” when they pass through an opening in a barrier.
3 Young's two slit interference pattern Young's two slit interference pattern Small openings allow only a single wavelet each (idealized) The pattern we can see consists of bright and dark “fringes” → bright spots, constructive interference, same phase → dark spots, destructive interference, half phase d sin = m d sin = m 1 2 

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4 Graph of intensity pattern from two wavelets (Young) Graph of intensity pattern from two wavelets (Young) We found the intensity on the viewing screen by finding the phase difference φ between the two wavelets at every point on the viewing screen. = 2 d sin I = 4 I 0 cos 2 1 2  E x ,t = 2 E max cos 1 2  sin kx − t 1 2  I 0 = 1 2 c 0 E max 2
5 One more example: interference from thin films One more example: interference from thin films • Why do we see swirling, rainbow colors on a soap bubble? Interference : reflected waves at interface → phase difference due to ΔL and reflection → different wavelengths are interfering constructively on your retina

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6 Phase difference due to reflection Phase difference due to reflection • Last time: light passing through materials of different index of refraction will accrue a phase difference, in general • Today: light that reflects off a surface of different index of refraction has a phase change of either zero or a half- wavelength → Depends on indices of materials n 2 > n 1 → reflected light accrues a half-wavelength phase difference n 2 < n 1 → reflected light accrues no phase difference “higher means half” n 1 n 2 n 3
Most common scenario: air → larger n → air Most common scenario: air → larger n → air Assume film thickness L, approximate the distance traveled by the wave inside n 2 is 2L Reflection at first interface → phase shifted by λ/2 Reflection at second interface → phase shifted by 0 Refraction: in region 2, wavelength contracts to λ/n 2 Constructive condition: Destructive condition: Not the general case!! n

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Lecture 2 - Diffraction Lecture 4 Diffraction Reading Ch 36...

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