7.6.2: Explorations
- Page ID
- 33421
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Exploration 1: Varying Numbers and Orientations of Sources
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.
Two sources of light waves of equal frequency and amplitude are shown. In the amplitude view the greatest amplitude is represented by white, negative amplitudes are represented by black, and areas with zero amplitude are represented by gray. In the intensity view the greatest magnitude of the amplitude (positive or negative) is represented by white, while black shows regions of zero amplitude (position is given in nanometers). Restart.
- What would the pattern look like (in both the amplitude and intensity views) if one source were removed? Answer: view with one source.
- What is the wavelength? (Check both the amplitude and intensity views.)
- In which view do you measure the wavelength by measuring the distance from the middle of the white band to the middle of the adjacent white band, and in which view do you have to measure the distance across two white bands (or black bands)? Why?
- What would the pattern look like if the two sources were in phase with each other but rotated \(90^{\circ}\) to lie on the \(x\) axis? Answer: rotate sources.
- Explain why the pattern looks the way it does.
Exploration authored by Melissa Dancy and Anne J. Cox.
Exploration 2: Changing the Separation Between Sources
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.
Two sources of light waves of equal frequency and amplitude are shown. The magnitude of the electric field is represented by the light and dark areas. The lighter the spot, the greater the magnitude of the electric field at that spot (position is given in nanometers).
Begin with the 0.5 wavelength separation animation. The sources are separated by one half the wavelength of the light.
- Predict what pattern would be seen if the source separation was increased to one wavelength. AFTER you have made your prediction and written down your reasoning, check to see if you were correct. If you were incorrect, reexamine your reasoning by looking at the one wavelength separation animation.
- When you feel confident in your understanding, test it by predicting the pattern if the source separation is \(1.5\) wavelengths. Check your prediction with the 1.5 wavelength separation animation.
- As a final test, predict the pattern for separations of \(2\) and \(2.5\) wavelengths. Check your prediction with the two wavelength separation and 2.5 wavelength separation animations.
- If a screen is placed on the right-hand side of the viewing window, how would the interference pattern change as the distance between the sources is increased?
Exploration authored by Melissa Dancy.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.