7.7.3: Problems
- Page ID
- 33426
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Exercise \(\PageIndex{1}\): Rank waves in ripple tanks by slit width
The animation shows waves from a single slit (which is underneath the red, blue, or green stripe). Restart. Rank the animations from the smallest slit to the largest slit.
This applet calculates seven frames and then runs continuously. For a large number of sources, or for very small wavelengths, this calculation can take some time, so let the applet finish calculating all sevenf frames.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{2}\): Rank waves in ripple tanks by slit width
The animation shows waves from a single slit (which is underneath the red, blue, or green stripe). Restart. Rank the animations from the smallest slit to the largest slit.
This applet calculates seven frames and then runs continuously. For a large number of sources, or for very small wavelengths, this calculation can take some time, so let the applet finish calculating all seven frames.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{3}\): Determine the slit width
The animation shows the interference (diffraction) pattern from light exiting a single slit located underneath the green strip (position is given in microns [\(10^{-6}\) meters]). In this animation, the greatest amplitude of the wave is represented by white, negative amplitudes are represented by black, and areas with zero amplitude are represented by gray. Restart. Determine the size of the slit.
This applet calculates seven frames and then runs continuously. For a large number of sources, or for very small wavelengths, this calculation can take some time, so let the applet finish calculating all seven frames.
Problem authored by Wolfgang Christian and Anne J. Cox.
Exercise \(\PageIndex{4}\): Wavelength of light through a single slit
This animation models light hitting a single slit. You can change the width of the slit and use the protractor to measure angles (position is given in centimeters and angle is given in degrees). Restart. What is the wavelength of the light?
We have made the higher-order diffraction patterns easier to see by brightening them (since the higher-order terms are very dim).
Problem authored by Anne J. Cox.
Script authored by Anne J. Cox and Morten Brydensholt.
Exercise \(\PageIndex{5}\): Wavelength of light through a diffraction grating
This animation models a diffraction grating that is a series of parallel slits in a material. You can change the slit spacing and see the first- and second-order maxima (position is given in centimeters and angle is given in degrees). Restart. What is the wavelength of the light passing through the diffraction grating?
Problem authored by Anne J. Cox.
Script authored by Anne J. Cox and Morten Brydensholt.
Exercise \(\PageIndex{6}\): Number of slits per millimeter in diffraction grating
This animation models a diffraction grating that is a series of parallel slits in a material. As you change the wavelength, notice where the bright spots are. You can move the protractor around to measure angles (position is given in centimeters and angle is given in degrees). Restart. How many slits per millimeter does the diffraction grating have?
Problem authored by Anne J. Cox.
Script authored by Anne J. Cox and Morten Brydensholt.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.