7.5.3: Problems
- Page ID
- 33418
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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 \(\PageIndex{1}\): Check vision, prescribe glasses
This animation models the eye (position is given in arbitrary units and angle is given in degrees). The slider can be used to simulate the eye's ability to accommodate. When the eye is in a relaxed state, the focal length of the lens system of the eye is taken to be one. Notice that as the eye accommodates, focusing on nearby objects, the focal length of the eye decreases. The location of the near source can be changed by dragging the source. The focal length of the eyeglass can be altered by clicking on the eyeglass and then dragging the hotspots. Restart.
- Is the eye represented in the animation normal, nearsighted, or farsighted?
- If the eye is nearsighted, what power eyeglasses should be used for normal vision? (The eye can see faraway objects when relaxed and also focus on an object at \(x = 2.0\).)
- If the eye is farsighted, what power eyeglasses should be used to allow the person to see an object at \(x = 2.0\)? Would a farsighted person with these glasses still be able to focus on a faraway object? Why are farsighted individuals often prescribed bifocals?
Problem authored by Melissa Dancy and Wolfgang Christian.
Exercise \(\PageIndex{2}\): Check vision, prescribe glasses
This animation models the eye (position is given in arbitrary units and angle is given in degrees). The slider can be used to simulate the eye's ability to accommodate. When the eye is in a relaxed state, the focal length of the lens system of the eye is taken to be one. Notice that as the eye accommodates, focusing on nearby objects, the focal length of the eye decreases. The location of the near source can be changed by dragging the source. The focal length of the eyeglass can be altered by clicking on the eyeglass and then dragging the hotspots. Restart.
- Is the eye represented in the animation normal, nearsighted, or farsighted?
- If the eye is nearsighted, what power eyeglasses should be used for normal vision? (The eye can see faraway objects when relaxed and also focus on an object at \(x = 2.0\).)
- If the eye is farsighted, what power eyeglasses should be used to allow the person to see an object at \(x = 2.0\)? Would a farsighted person with these glasses still be able to focus on a faraway object? Why are farsighted individuals often prescribed bifocals?
Problem authored by Melissa Dancy and Wolfgang Christian.
Exercise \(\PageIndex{3}\): Check vision, prescribe glasses
This animation models the eye (position is given in arbitrary units and angle is given in degrees). The slider can be used to simulate the eye's ability to accommodate. When the eye is in a relaxed state, the focal length of the lens system of the eye is taken to be one. Notice that as the eye accommodates, focusing on nearby objects, the focal length of the eye decreases. The location of the near source can be changed by dragging the source. The focal length of the eyeglass can be altered by clicking on the eyeglass and then dragging the hotspots. Restart.
- Is the eye represented in the animation normal, nearsighted, or farsighted?
- If the eye is nearsighted, what power eyeglasses should be used for normal vision? (The eye can see faraway objects when relaxed, and also focus on an object at \(x = 2.0\).)
- If the eye is farsighted, what power eyeglasses should be used to allow the person to see an object at \(x = 2.0\)? Would a farsighted person with these glasses still be able to focus on a faraway object? Why are farsighted individuals often prescribed bifocals?
Problem authored by Melissa Dancy and Wolfgang Christian.
Exercise \(\PageIndex{4}\): Location of near point
This animation models the eye (position is given in arbitrary units and angle is given in degrees). The slider can be used to simulate the eye's ability to accommodate. When the eye is in a relaxed state, the focal length of the lens system of the eye is taken to be one. Notice that as the eye accommodates, focusing on nearby objects, the focal length of the eye decreases. The location of the near source can be changed by dragging the source. Restart. What is the location of the near point of the eye?
Problem authored by Melissa Dancy and Wolfgang Christian.
Exercise \(\PageIndex{5}\): Microscope
Two lenses, an eyepiece and an objective are used to make a microscope (position is given in centimeters and angle is given in degrees). You may focus the microscope by click-dragging the object into position. Restart. Where should the object be placed for optimal viewing by a relaxed eye?
Problem authored by Melissa Dancy and Wolfgang Christian.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.