Phys 115 1st Edition Lecture 19Outline of Last Lecture I. Optics of the eye II. Correction of visual defectsIII. Chromatic aberrationOutline of Current Lecture IV. Superposition of wavesV. Two-slit interferenceVI. Multi-slit interferenceVII. Diffraction gratingsCurrent Lecture- Recall from last semester that two waves superpose when they meet: total is sum of contributions from the two waves.- Constructive interference: waves add- Destructive interference: waves cancel- Sources in phase: emit crests at same timeThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Constructive interference: crests coincide with crests - Occurs where path-length difference = mλ(m = 0, 1, 2, …)- Resulting wave has larger amplitude than individual waves- Destructive interference: crests coincide with troughs - Occurs where path-length difference = (m+ ½)λ(m = 0, 1, 2, …)- Resulting wave is zero (waves cancel out)- View from above:o Constructive interference where r2 – r1 = mλo Destructive interference where r2 – r1 = (m+ ½)λ- Waves spread out as they go through openings of size comparable to wavelength- Same for light waves if slit width is ~ λ.- Visible light wavelength:o ~ 400 – 800 nm- Light wave passing through two slits produces an interference pattern on a distant screen (L>>d)- Slits act as sources, in phase- r2 – r1 = dsinθ- Constructive interference (bright fringe) where r2 – r1 =dsinθ = mλ- Destructive interference (dark fringe) where r2 – r1 =dsinθ = (m+ ½)λ- Angles for constructive interference (bright fringes): sinθ = mλ/do L >>d so angles are small: sinθ ≈ tanθo tanθ = y/L = mλ/do Fringes labeled by index mo Maximum possible value of m =
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