7.3.3: Problems
- Page ID
- 33409
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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 \(\PageIndex{1}\): Find index of refraction, two mediums
A beam of parallel rays is shown passing through a medium surrounded by air. Both the position of the source and the angle of the source rays can be adjusted by click-dragging the circular hotspots. You can move the pink protractor around and use it to measure angles (position is given in meters and angle is given in degrees). Restart.
- What is the index of refraction of the inner medium?
- What is the angle of total internal reflection for the inner medium?
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{2}\): Find index of refraction, one medium
A light beam source, in air, is incident on a substance of unknown index of refraction. You can click-drag both the position and the ray angle of the beam. You can move the pink protractor around and use it to measure angles (position is given in meters and angle is given in degrees). Restart. What is the unknown substance?
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{3}\): Where is the image located?
A source of light is shown in a medium. Angles can be measured by click-dragging the movable green protractor (position is given in meters and angle is given in degrees). Restart. Where is the image located as seen by someone looking into the substance from the right?
Problem authored by Melissa Dancy and Wolfgang Christian.
Exercise \(\PageIndex{4}\): Find index of refraction of a lens
What is the index of refraction of the lens? Restart.
Problem authored by Melissa Dancy and Wolfgang Christian.
Exercise \(\PageIndex{5}\): Size of a fish's world
A fish in a tank is shown. Both the position of the source and the angle of the source rays can be adjusted by click-dragging the circular hotspots. You can use the movable green protractor and click-drag to measure angles (position is given in centimeters and angle is given in degrees). Restart.
- When the fish's eye is \(1\text{ cm}\) from the edge, how big is the circle through which the fish sees the world outside the fish tank when he looks straight ahead (to the right in the animation)?
- Find an expression for the size of the circle through which the fish sees the outside world as a function of how far away the fish is from the right edge of the tank.
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{6}\): Rank the indices of refraction
Rank the media from smallest index of refraction to largest. You can change the angle of the beam by clicking on the beam source and then click-dragging its hotspot. You can use the movable pink protractor and click-drag to measure angles (angle is given in degrees). Restart.
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{7}\): Total internal reflection
Four materials are next to each other, and the change in the index of refraction from one to the next is the same. (In other words, if the index of refraction of region \(A\) is \(1.5\) AND the index of refraction of region \(B\) is \(2\), then the index of refraction in region \(C\) is \(2.5\), and so forth.) You can move the beam source, but you cannot change the angle of the light. You can use the movable green protractor and click-drag to measure angles (angle is given in degrees). Restart.
What is the index of refraction of region \(D\)? Explain your observations as you drag the source through each of the different materials. (Why is there total internal reflection between some interfaces, but not others?)
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{8}\): Wavefronts on a medium
The animation models wave fronts in air entering a region of unknown index of refraction. Assume the wave fronts are traveling at the speed of light (in air) before entering the unknown region (position is given in units normalized to the speed of light in air). Restart.
- Why are the wave fronts closer together in the unknown medium?
- What is the index of refraction of the unknown medium?
- In terms of the speed of light, how fast are the wave fronts traveling inside the medium?
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{9}\): Huygens' principle and refraction
The animation shows a wave front passing from one medium to another. Huygens' principle is applied at the boundary between the mediums. Restart.
- What happens to the wavelength for the refracted light wave when \(n_{2} > n_{1}\)?
- What happens to the wavelength for the refracted light wave when \(n_{2} = n_{1}\)?
- What happens to the wavelength for the refracted light wave when \(n_{2} < n_{1}\)?
- What happens to the frequency of the refracted light wave in each of the given situations?
Problem authored by Morton Brydensholt and modified by Melissa Dancy.
Exercise \(\PageIndex{10}\): Refraction and colors of light
Light rays from a beam source, initially in air, are shown incident on a piece of glass. You can change the wavelength of light by moving the slider. Restart. Which animation is correct? Explain.
Problem authored by Anne J. Cox.
Script authored by Morten Brydensholt and modified by Anne J. Cox.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.