4.1: Reflections and phase
- Page ID
- 128461
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)We revise reflection and transmission at the junction between a light string and a heavy string. Analogously, going from a transparent medium with low refractive index to one with high n, the reflected light wave has a 90° phase change. From high n to low, the reflected light has no phase change. In both cases, there is no phase change in the transmitted wave. We briefly view reflections in a thin film and revisit Young’s experiment.
We revise Young's experiment.
Revise reflections in waves on strings.
Phases of reflection and transmission at interfaces between transparent media.
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Links to related material |
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| Introduction to Young's experiment Young's experiment with water waves. The geometry: d sin θ = mλ for constructive interference; d sin θ = (m+½)λ for destructive interference. Phasor addition: calculating I(φ). Measuring I(φ). Interference: why does more light sometimes make the pattern darker? |
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| Young's experiment with single photons. Does the interference pattern still appear when we do it one photon at a time? Movie clips showing how individual photon capture events build up the histogram that forms the diffraction and interference patterns. Discussion of the photon puzzles. |
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| Molecules and photons Introducing the idea of quantisation: molecules as quanta of matter. Light and photons. Energy depends on wavelength. The photoelectric effect. Black body radiation |
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| Reflections and phases The phases of reflection and transmission at interfaces in one dimension: analogies with light. Animations showing phase relations for reflections air to glass and glass to air |
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| Thin film interference and reflections Reflections and phase differences. Constructive and destructive interference. Interference colours in soap bubbles. Black films. Iridescence. |
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| Soap bubbles The thinning of soap films. Surface tension and the forces involved. Minimal surfaces and geometry |
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| Non-reflective coatings. Optical pathlenght. Non-reflective coatings as examples of thin film interference: intermediate refractive index, optical pathlength difference = λ/2 for medium optical wavelengths. |
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| Coherence length An important concent in interference: when differences in optical pathlength exceed the coherence length, phases are no longer correlated so interference is not observed. |
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| Newton's rings A thin film of air between a plano-convex lens and a glass flat. Here, thin film interference produces concentric rings of destructive and constructive interference. From the wavelength and the radii of the interference rings, we determine the radius of curvature of the lens. |
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Interference Experiments |
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