7.4.3: Problems
- Page ID
- 33413
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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 \(\PageIndex{1}\): Hidden lenses, point sources
Four regions are hidden by curtains. You can drag the source of light to any location (position is given in meters).
- What is behind each curtain?
- Rank the objects in terms of their focal lengths from smallest to largest (most negative to most positive).
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{2}\): Hidden lenses, mixed sources
Four regions are hidden by curtains. The light sources are dragable. The arrow represents an object, and the fainter arrow represents its image (position is given in meters).
- What is behind each curtain?
- Rank the objects in terms of their focal lengths, from smallest to largest (most negative to most positive).
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{3}\): Hidden lenses, point sources
Four lenses are represented by vertical lines. You can drag the light sources to any location (position is given in meters). Rank the lenses in terms of their focal lengths, from smallest to largest (most negative to most positive).
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{4}\): Focal length of converging lens
A lens is shown with a light source. The light source is constrained to move along the line \(y = 0.4\text{ m}\) (position is given in meters). Restart. What is the focal length of the lens?
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{5}\): Focal length of lens system
A dragable light source is shown with two lenses (position is given in meters). Restart.
- What is the focal length of the lens system?
- What is the focal length of each individual lens?
Exercise \(\PageIndex{6}\): Image location, beam source
A lens is shown with a source of parallel light rays. You can drag the source and change the orientation of its rays by dragging its hotspots (position is given in meters). Restart.
- If an object were placed at \(x = 0\text{ m}\), where would the image of that object be located?
- Would the image be upright or inverted?
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{7}\): Image location, point source
A lens is shown with a point source of light. You can drag the source and change the orientation of its rays by dragging its hotspots (position is given in meters). Restart.
- If an object were placed at \(x = 0\text{ m}\), where would the image of that object be located?
- Would the image be upright or inverted?
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{8}\): Find the focal length of each lens in the 2-lens system
A light source is located to the left of two lenses (position is given in centimeters). You can click-drag either lens through a limited range of \(x\) positions. Find the focal length of each lens. Restart.
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{9}\): Find the focal length of each lens in the 2-lens system
A light source is located to the left of two lenses (position is given in centimeters). You can click-drag the left lens through a limited range of \(x\) positions. The right lens will move in tandem. Find the focal length of each lens. Restart.
Exercise \(\PageIndex{10}\): Find the focal length of each lens in the 3-lens system
Three lenses are shown with a point source of light. You can drag the source and lenses with some restrictions (position is given in meters). Restart. Find the focal length of each lens.
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{11}\): Build a converging lens
Light rays from a point source, initially in air, are incident on a lens made from a material with an index of refraction of \(2.5\) (position is given in centimeters). The radius of curvature of the left side of the lens is \(-10\text{ cm}\) (\(10\text{-cm}\) radius and concave, so rays diverge upon entering it). You can change the radius of the right side. Restart. Build a lens so that the light rays from the point source will converge on the green screen.
- What is the focal length of this lens?
- Calculate the radius of curvature of the right side of the lens, then test your calculation.
Problem authored by Anne J. Cox.
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