5.3: Diffraction gratings
- Page ID
- 128469
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Diffraction gratings. Phasor addition shows how adding more slits gives narrower, brighter diffraction peaks. A diffraction grating has many equally spaced slits; it can measure \(\lambda\) of sources precisely in transmission or reflection. Incandescent sources have continuous spectra. Electrons in atoms have discrete energies governed by quantum mechanics. Consequently, atoms have spectra with discrete emission and absorption lines. Helium was discovered by its spectral lines in light from the sun, before it was observed on Earth.
- Adding more slits gives narrower, brighter peaks.
- A diffraction grating has many slits and so can measures \(\lambda\). precisely.
- Incandescent spectra are continuous. Gases have spectra with discrete emission and absorption lines.
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Links to related material |
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| Diffraction, shadows, beams, Huygens' construction. Diffraction of light and sound. Water waves in a ripple tank. Shadows and beams with water waves of short wavelength. Diffraction at longer wavelengths. X-ray, neutron and electron diffraction |
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| Diffraction from a single slit. Young's experiment with finite slits. Diffraction from a single slit:Huygens' construction. Phasor diagrams give Iq. Varying the slit width. Young's experiment with finite slit width: Iq shows both interference and diffraction effects. |
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| The quantum mechanics of cricket A light-hearted discussion to illustrate why we don't notice quantum interference in everyday life. |
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| Diffraction gratings and spectroscopy. Adding phasors with 2, 3, 4 and many slits: Diffraction gratings. Diffraction from monochromatic sources. Continuous spectra and line spectra, absorption and emission spectra. The hydrogen spectrum and the origins of quantum mechanics. |
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| Poisson-Arago dot The bright dot at the centre of the shadow: Poisson's argument against the wave nature of light. A modern recreation of Arago's experiment. |
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| Rayleigh criterion and the Airy disc: Aperture and resolution Circular apertures in optics. Diffraction pattern from a circular aperture. The Airy disc. Resolving two point sources: Rayleigh's criterion. When is the eye diffraction limited? The resolution of telescopes. Radio telescopes and arrays |
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| X-ray diffraction: Bragg's law The atomic lattice as a diffraction grating. Diffraction requires wavelengths less than 0.1 nm. X-ray diffraction. |
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| Holography Forming a hologram: beam splitter, object and reference beams, interference at the film. Recreating a hologram: coherence beam and hologram plate. |
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| Diffraction Experiments Single slit diffraction, diffraction gratings. |
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