7.2.3: Problems
- Page ID
- 33405
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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 \(\PageIndex{1}\): Focal length of concave mirror, point source
A point source is located to the left of a mirror. You can drag this point source to any position (position is given in meters and angle is given in degrees). Restart. Find the focal length of the mirror.
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{2}\): Focal lengh of concave mirror, beam source
A beam of light is incident upon a mirror. You can click-drag both the position and angle of this beam (position is given in meters and angle is given in degrees). Restart. Find the focal length of the mirror.
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{3}\): Image in concave mirror
The animation shows an object and its image (position is given in meters and angle is given in degrees). You can click-drag the top of the arrow-shaped object. Restart.
Which, if any, of the following statements are true for this mirror?
- The magnification changes sign when the tip of the arrow is dragged below the principal axis.
- Light rays leaving the tip of the arrow always pass through the image.
- Real images are always inverted, while virtual images are always upright.
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{4}\): Focal length of concave mirror, object source
A dragable object is located to the left of a mirror. You can click-drag both the position and height of the object (position is given in meters and angle is given in degrees). Restart. Find the focal length of the mirror.
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{5}\): Focal length of convex mirror, object source
A dragable object is located to the left of a mirror (position is given in meters and angle is given in degrees). Restart. Find the focal length of the mirror.
Problem authored by Melissa Dancy.
Exercise \(\PageIndex{6}\): Focal length of convex mirror, point source
This animation has a point source, a beam source, and a mirror. You can also find an angle or create a line with an angle by moving the pink protractor and click-dragging to change the angle (position is given in meters and angle given in degrees). Restart. Which dot is sitting at the focal point of the mirror?
Exercise \(\PageIndex{7}\): Objects in mirror are closer than they appear
Many side mirrors on cars have a label that says "objects in mirror are closer than they appear." What type of mirror is it? The animation has an object and a mirror (position is given in meters and angle given in degrees). You can choose the type of mirror you want to try. Restart.
- To determine what type of mirror a side mirror on a car is, first consider (from your experience) whether the image in the mirror is upright or inverted? Does your answer change as the object changes distance from the mirror? Therefore, which type of mirror can't it be?
- For objects to be "closer than they appear," could it mean (1) that the image distance is longer than the object distance (so you perceive the object to be farther away) and/or (2) that the image is smaller (since we judge distances by relative sizes of objects). Therefore, which type of mirror can't it be (which mirror does not have a smaller image or a longer image distance)?
- For the type of mirror that the car's side mirror is, then, why are "objects closer than they appear"?
Problem authored by Anne J. Cox.
Exercise \(\PageIndex{8}\): Hidden mirrors, point source
Four regions are hidden by a curtain. You can drag the source of light to any location and adjust the beam width (position is given in meters and angle is given in degrees).
- What is behind each curtain?
- Rank the objects in terms of their focal lengths, from smallest to greatest.
Problem 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.