\documentclass{sebase}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{SEART}

%TCIDATA{TCIstyle=article/art4.lat,SEART,SEART}

%TCIDATA{Created=Tue Sep 23 17:59:11 1997}
%TCIDATA{LastRevised=Wed Dec 03 21:03:59 1997}

\input{tcilatex}
\begin{document}

\SetTitle{Phy206 Exam III}
\SetAuthor{T. Curtright}
\Setdate{26 November 1997}
\TitlePage{This is a ``closed book'', multiple-choice exam. You are NOT allowed to use
any notes. \emph{Circle only one answer} out of the five choices for each
problem. Do ALL problems.\\
Sometimes, usually by accident, none of the listed answers is correct. If
you firmly believe that this is the case, then you should \emph{write-in}
what you believe to be \emph{the correct answer}.\\
You may ask the instructor questions, especially if you think a problem is
not clearly stated.\\
\bigskip \bigskip Good luck!\\
\textbf{\ \bigskip \bigskip ``On my honor, I have neither given nor received
any aid on this examination.''}\\
\bigskip
Name:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\
\bigskip ID \#:
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}

NOTE: This is the exam key. The answer (a) is correct for each question.

\smallskip \eject 
A light ray passes through air ($n=1$) and strikes the top of a plane sheet
of glass. The glass sheet is of constant thickness, $d$, and has index of
refraction $n>1$. The striking light ray makes an angle $\theta $ with
respect to the normal to the plane sheet. Part of the ray is reflected. Part
of the ray penetrates the glass sheet.

\vspace*{\fill}\noindent [1] What angle $\Theta $ does the penetrating ray
make with respect to the normal to the sheet?

(a) $\Theta =\arcsin \left( \frac{1}{n}\,\sin \theta \right) \;\;\;$(b) $%
\Theta =\arccos \left( \frac{1}{n}\,\cos \theta \right) \;\;\;$(c) $\Theta
=\theta $

(d)$\;\Theta =\arcsin \left( n\,\sin \theta \right) \;\;\;$(e) $\Theta
=\arccos \left( n\cos \theta \right) $

\vspace*{\fill}\noindent [2] The penetrating ray crosses the interior of the
glass sheet and is reflected from the bottom, then it crosses the interior
again and re-emerges into the air at the top of the sheet. How much
distance, $s,$ has the penetrating ray traveled within the glass sheet?

(a) $s=\frac{2dn}{\sqrt{n^{2}-\sin ^{2}\theta }}\;\;\;$(b) $s=\frac{2dn}{%
\cos \theta }\;\;\;$(c) $s=2dn\cos \theta $

(d)$\;s=\frac{dn}{\cos \Theta }\;\;\;$(e) $s=2dn\cos \Theta $

\vspace*{\fill}\noindent [3] If the light has a wavelength $\lambda $ in the
air, and is described by a simple sine wave, what phase $\Phi $ does the
penetrating wave acquire as a result of its travel through the glass sheet?

(a) $\Phi =2\pi ns/\lambda \;\;\;$(b) $\Phi =2\pi s/\lambda \;\;\;\;$(c) $%
\Phi =2\pi s/\left( n\lambda \right) \;$

(d) $\Phi =2\pi n\lambda /s\;\;\;\;\;$(e) $\Phi =2\pi \lambda /\left(
ns\right) $

\vspace*{\fill}\noindent [4] What distance $x$ does the wavefront outside
the glass move as a result of advancing from the point where the ray
penetrated the glass to the point where the penetrating ray re-emerged?

(a) $x=\frac{2d\sin ^{2}\theta }{\sqrt{n^{2}-\sin ^{2}\theta }}\;\;$(b) $%
x=\left( 2d\sin \theta \right) /n\;\;\;$(c) $x=2d\sin ^{2}\theta $

(d)$\;x=2d\sin \theta \;\;\;$(e) $x=2dn\sin \theta $

\vspace*{\fill}\noindent [5] If this wavefront outside the glass is now
reflected at the point where the penetrating ray re-emerges, what is the
total phase difference $\Delta \varphi $ between this reflected wave and the
re-emergent penetrating wave?

(a) $\Delta \varphi =2\pi x/\lambda -\Phi +\pi \;\;\;$(b) $\Delta \varphi
=2\pi x/\lambda -\Phi \;\;\;$(c) $\Delta \varphi =2\pi x/\lambda +\Phi -\pi $

(d)$\;\Delta \varphi =2\pi x/\lambda +\Phi \;\;\;$(e)$\;\Delta \varphi =0$

\eject 

A thin lens of focal length $f_{lens}=50\;cm$ is located at $x=0,$ on the $x$%
-axis, in front of a convex spherical mirror located at $x=50\;\,cm$, also
on the $x$-axis. The radius of curvature of the mirror has magnitude $\left|
R\right| =50\;cm$. A real object is placed on the $x$-axis at $x=-100\;cm$.

\vspace*{\fill}\noindent [1] What is the focal length of the mirror?

(a) $f_{mirror}=-25\;cm\;\;\;$(b) $f_{mirror}=25\;cm\;\;\;$(c) $%
f_{mirror}=50\;cm\;\;\;$

(d) $f_{mirror}=-50\;cm\;\;\;$(e)\ $f_{mirror}=100\;cm$

\vspace*{\fill}\noindent [2] What is the location, on the $x$-axis, of the
final image for this combination of object, lens, and mirror?

(a) $x=-100\;cm\;\;\;$(b) $x=100\;cm\;\;\;$(c) $x=-50\;cm\;\;\;$

(d) $x=50\;cm\;\;\;$(e) $x=0\;cm\;\;\;$

\vspace*{\fill}\noindent [3] Which of the following describes the final
image?

(a) real and inverted\ \ \ (b) real and upright\ \ \ (c) virtual and
inverted\ \ \ 

(d) virtual and upright\ \ \ (e) nonexistent

\vspace*{\fill}\noindent [4] What is the magnification of the final image?

(a) $m=-1.0\;\;\;$(b) $m=1.0\;\;\;$(c) $m=-2.0\;\;\;$(d) $m=2.0\;\;\;$(e) $%
m=0\;\;\;$

\vspace*{\fill}\noindent [5] If the convex mirror is replaced by a concave
mirror with the same value for $\left| R\right| $, but which is then moved
to a new location on the $x$-axis at $x=100\;cm$, what is the location of
the new final image?

(a) $x=-100\;cm\;\;\;$(b) $x=100\;cm\;\;\;$(c) $x=-50\;cm\;\;\;$

(d) $x=50\;cm\;\;\;$(e) $x=0\;cm$

\vspace*{\fill}\eject 

A very narrow beam of white light from a very distant point source is
incident normally from above and strikes a small spot on the surface of a
Beatles CD as it lies on a table top. The tracks on the CD are separated by
a distance $d=1.0\;\mu m$.

\vspace*{\fill}\noindent [1] What is the condition for light of wavelength $%
\lambda $ to be ``diffracted'' from the surface of the CD at an angle $%
\theta $ with respect to the normal, and in a direction perpendicular to the
tracks, so that a maximum intensity is obtained? (In these answers, $m$ is
an arbitrary integer.)

(a) $d\,\sin \theta =m\lambda \;\;$(b) $d\,\cos \theta =m\lambda \;\;\;$(c)$%
\;d\,\sin \theta =(m+1/2)\lambda \;\;$

(d) $d\,\cos \theta =(m+1/2)\lambda \;\;\;$(e)\ $d\tan \theta
=(m+1/2)\lambda $

\vspace*{\fill}\noindent [2] What is the minimum non-zero angle $\theta
_{blue}$ for which the diffracted light looks blue, with a wavelength $%
\lambda _{blue}=450\;nm$?

(a) $\theta =\allowbreak 0.\,47\;radians\;\;\;$(b) $\theta =\allowbreak
1.\,10\;radians\;\;\;$(c) $\theta =\allowbreak 0.\,23\;radians$

(d) $\theta =\allowbreak 1.\,34\;radians\;\;\;$(e) $\theta \allowbreak
=\allowbreak 0.\,22\;radians$

\vspace*{\fill}\noindent [3] What is the minimum non-zero angle $\theta
_{red}$ for which the diffracted light looks red, with a wavelength $\lambda
_{red}=700\;nm$?

(a) $\theta =\allowbreak 0.\,78\;radians$\ \ (b) $\theta =0\allowbreak
.\,80\;radians$\ \ \ (c) $\theta =0\allowbreak .\,25\;radians$\ 

(d) $\theta =0\allowbreak .\,31\;radians$\ \ \ (e) $\theta =0\allowbreak
.\,81\;radians$

\vspace*{\fill}\noindent [4] What is the minimum non-zero angle $\theta
_{green}$ for which the diffracted light looks green, with a wavelength $%
\lambda _{green}=500\;nm$?

(a) $\theta =\allowbreak 0.\,52$\ $radians$\ \ \ (b) $\theta =\allowbreak
1.\,04\;radians$\ \ \ (c) $\theta =0\allowbreak .\,25\;radians$\ 

(d) $\theta =\allowbreak 1.\,32\;radians$\ \ \ (e) $\theta =\allowbreak
0.\,24\;radians$

\vspace*{\fill}\noindent [5] What is the second smallest non-zero angle $%
\theta _{blue\;2}$ for which the diffracted light also looks blue, with a
wavelength $\lambda _{blue}=450\;nm$?

(a) $\theta =\allowbreak 1.\,12\;radians\;\;$\ (b) $\theta =0\allowbreak
.\,45\;radians$\ \ \ (c) $\theta =\allowbreak 0.\,74\;radians$

(d) $\theta =\allowbreak 0.\,83\;radians$\ \ (e) $\theta =\allowbreak
0.\,59\;radians$

\vspace*{\fill}\eject 

Yellow-green light of wavelength $\lambda =520\;nm$ illuminates a planar
screen in which there are two identical parallel slits of width $a=0.04\;mm$
and separation $d=0.12\;mm$. The incoming light rays are perpendicular to
the plane of the screen containing the slits. Light passes in equal amounts
through each of the slits and produces an interference pattern on another
``viewing'' screen parallel to the first but at a distance $L=1.0\;m$ away.
The distance along the viewing screen, measured from its center and
perpendicular to the parallel slits, is called $x$.

\vspace*{\fill}\noindent [1] Which of the following figures best illustrates
the interference pattern produced on the viewing screen as a function of $x$?

(a)\FRAME{itbpF}{3in}{0.6564in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 0.6564in;depth 0in;display
"USEDEF";plot_snapshots TRUE;function \TEXUX{$\cos ^{2}\left( 3\pi x\right)
\sin ^{2}\left( \pi x\right) \left/ \left( \pi x\right) ^{2}\right.
$};linecolor "black";linestyle 1;linethickness 1;pointstyle "point";xmin
"-2.49636";xmax "2.62774";xviewmin "-2.5";xviewmax "2.5";yviewmin
"-0.01997";yviewmax "1.02";viewset"XY";rangeset"X";phi 45;theta 45;plottype
4;numpoints 99;axesstyle "none";xis \TEXUX{x};var1name
\TEXUX{$x$};valid_file "T";tempfilename
'C:/SWP25/docs/EK8IYF0A.wmf';tempfile-properties "XP";}}(b)\FRAME{itbpF}{3in%
}{0.6564in}{0in}{}{}{}{\special{language "Scientific Word";type
"MAPLEPLOT";width 3in;height 0.6564in;depth 0in;display
"USEDEF";plot_snapshots TRUE;function \TEXUX{$\cos ^{2}\left( 3\pi x\right)
$};linecolor "black";linestyle 1;linethickness 1;pointstyle "point";xmin
"-2.49636";xmax "2.62774";xviewmin "-2.5";xviewmax "2.5";yviewmin
"-0.01997";yviewmax "1.02";viewset"XY";rangeset"X";phi 45;theta 45;plottype
4;numpoints 99;axesstyle "none";xis \TEXUX{x};var1name
\TEXUX{$x$};valid_file "T";tempfilename
'C:/SWP25/docs/EK8IZ90B.wmf';tempfile-properties "XP";}}

(c)\FRAME{itbpF}{3in}{0.6668in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 0.6668in;depth 0in;display
"USEDEF";plot_snapshots TRUE;function \TEXUX{$\sin ^{2}\left( \pi x\right)
\left/ \left( \pi x\right) ^{2}\right. $};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-2.49636";xmax "2.62774";xviewmin
"-2.5";xviewmax "2.5";yviewmin "-0.01997";yviewmax
"1.02";viewset"XY";rangeset"X";phi 45;theta 45;plottype 4;numpoints
99;axesstyle "none";xis \TEXUX{x};var1name \TEXUX{$x$};valid_file
"T";tempfilename 'C:/SWP25/docs/EK8J020C.wmf';tempfile-properties "XP";}}(d)%
\FRAME{itbpF}{3in}{0.6564in}{-0.0104in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 0.6564in;depth -0.0104in;display
"USEDEF";plot_snapshots TRUE;function \TEXUX{$\cos ^{2}\left( 3\pi x\right)
\sin ^{2}\left( \pi x\right) $};linecolor "black";linestyle 1;linethickness
1;pointstyle "point";xmin "-2.49636";xmax "2.62774";xviewmin "-2.5";xviewmax
"2.5";yviewmin "-0.01997";yviewmax "1.02";viewset"XY";rangeset"X";phi
45;theta 45;plottype 4;numpoints 99;axesstyle "none";xis \TEXUX{x};var1name
\TEXUX{$x$};valid_file "T";tempfilename
'C:/SWP25/docs/EK8J0S0D.wmf';tempfile-properties "XP";}}

(e)\FRAME{itbpF}{3in}{0.6668in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 0.6668in;depth 0in;display
"USEDEF";plot_snapshots TRUE;function \TEXUX{$\cos ^{2}(\pi x)$};linecolor
"black";linestyle 1;linethickness 1;pointstyle "point";xmin "-2.49636";xmax
"2.62774";xviewmin "-2.5";xviewmax "2.5";yviewmin "-0.01997";yviewmax
"1.02";viewset"XY";rangeset"X";phi 45;theta 45;plottype 4;numpoints
99;axesstyle "none";xis \TEXUX{x};var1name \TEXUX{$x$};valid_file
"T";tempfilename 'C:/SWP25/docs/EK8J1E0E.wmf';tempfile-properties "XP";}}

\vspace*{\fill}\noindent [2] Which of the following formulas best describes
the interference pattern produced on the viewing screen?

(a) $I=\mathcal{I}_{0}\;\cos ^{2}\left( \frac{\pi \,d\,x}{\lambda \,L}%
\right) \;\sin ^{2}\left( \frac{\pi \,a\,x}{\lambda \,L}\right) \left/
\left( \frac{\pi \,a\,x}{\lambda \,L}\right) ^{2}\right. \;\;\;$(b) $I=%
\mathcal{I}_{0}\;\cos ^{2}\left( \frac{\pi \,d\,x}{\lambda \,L}\right) $

(c)$\;I=\mathcal{I}_{0}\;\sin ^{2}\left( \frac{\pi \,a\,x}{\lambda \,L}%
\right) \left/ \left( \frac{\pi \,a\,x}{\lambda \,L}\right) ^{2}\right.
\;\;\;$(d)$\;I=\mathcal{I}_{0}\;\cos ^{2}\left( \frac{\pi \,d\,x}{\lambda \,L%
}\right) \;\sin ^{2}\left( \frac{\pi \,a\,x}{\lambda \,L}\right) $

(e) $I=\mathcal{I}_{0}\;\cos ^{2}\left( \frac{\pi \,a\,x}{\lambda \,L}%
\right) $

\vspace*{\fill}\noindent [3] What is the width of each of the ``two-slit''
interference peaks on the viewing screen?

(a)\ $\Delta x=\lambda L/d\;\;\;$(b) $\Delta x=\lambda L/a\;\;\;$(c)$%
\;\Delta x=2\lambda L/d\;\;\;$

(d)$\;\Delta x=2\lambda L/a\;\;\;$(e)$\;\Delta x=\lambda d/a$

\vspace*{\fill}\noindent [4] How many ``two-slit'' interference peaks lie
within what would be the ``single-slit'' diffraction peak?

(a) $5\;\;\;$(b) $4\;\;\;$(c) $3\;\;\;$(d) $2\;\;\;$(e) $1$

\vspace*{\fill}\noindent [5] Compared to the intensity in the center of the
viewing screen, $\mathcal{I}_{0}$, what is the intensity $I$ on the viewing
screen at a distance $x=\lambda L/2d$ from the center?

(a) $I/\mathcal{I}_{0}=0.00\;\;\;$(b) $I/\mathcal{I}_{0}=0.50\;\;\;$(c) $I/%
\mathcal{I}_{0}=0\allowbreak .\,75\;\;\;$

(d) $I/\mathcal{I}_{0}=0\allowbreak .\,91\;\;\;$(e) $I/\mathcal{I}_{0}=1.00$

\vspace*{\fill}\eject 

\end{document}