\section{L-3: Optical Instruments}\label{l03_optinst}

\noindent OBJECTIVE:
\begin{enumerate}
\item[] \latex{\vspace*{-.12in}} 
To construct a number of  optical instruments and measure 
magnification.\latex{\vspace*{-.06in}}
\end{enumerate}

\noindent APPARATUS:  
\begin{enumerate}
\item[] \latex{\vspace*{-.12in}} 
Identical to the of  L-2 plus white board,
achromatic doublets, Ramsden eyepiece. \latex{\vspace*{-.06in}}

\begin{description}
\item \latex{\vspace*{-.09in}}{\em SUGGESTION:}  In constructing an optical instrument catch the real image 
formed by the first lens on paper.  This location can tell where 
the next lens goes; e.g.~for a telescope or microscope place 
the next lens slightly less than its focal length beyond the 
first image.\latex{\vspace*{-.13in}}
\end{description}
\end{enumerate}

\noindent EXPERIMENTS: 
\begin{enumerate}
\item \latex{\vspace*{-.13in}}{\em Inverting~Telescope}
\begin{enumerate}
\item[A.] \latex{\vspace*{-.1in}}First measure the 
$f$ of a weak converging lens ($25 \leq f \leq 50$ cm) and 
of a strong converging lens ($f \sim 5$ cm).  The first lens ($f$ large) typically 
has the virtue of intercepting and focusing a fairly large area of light while the
second lens can be positioned to give a large virtual image (and hence magnification.)
Notice that if the first image, $q_1$is at a point $p_2 > f_2$ with respect to the
second lens you get a real, erect second image.  
If you are using the web-based
lab manual and desire a demonstration, click on the Inverting Telescope Demo button 
immediately below. 
%%%\input{toolbar/l03_j1}

Use you will use these two lenses to construct an astronomical (inverting) telescope.  
As an object, use the white board and scale while illuminated by a bright light. 
As a procedure for measuring the magnification, vary the space
between the objective L$_1$ and the eyepiece L$_2$ until 
the virtual image $I_2$ of scale S seen through L$_2$ lies in the plane of S
(i.e.~$p_1+d=|q_2|$).  As 
a sensitive test of this
there should be no parallax between the scale as seen 
directly by your eye 2 and the scale image seen by eye 1 thru the 
telescope as shown in Fig.~2.  Generally a person will adjust the eyepiece so
that the virtual image appears at the distance of most distinct vision ($\sim$25 cm).

\begin{figure}[!h] \centering
\latex{\vspace*{-.12in}}
\latex{\hspace*{.1in}\includegraphics[height=1.5in]{figs/l3-01.eps}}
\html{\includegraphics[height=2.2in]{figs/l3-01.eps}}
\latex{\vspace*{-.12in}}
\caption{The inverting telescope (not drawn to scale).}
\end{figure} 
\begin{figure}[!h] \centering
\latex{\vspace*{-.12in}}
\latex{\hspace*{.1in}\includegraphics[height=1.15in]{figs/l3-02.eps}}
\html{\includegraphics[height=1.6in]{figs/l3-02.eps}}
\latex{\vspace*{-.16in}}
\caption{View scale with one eye, then the other.}
\end{figure}

\item[B.] \html{\begin{tabular}{p{3.5in}l}}
\latex{\parbox[t][2.05in][t]{0.65\linewidth}}
{Adjust the telescope direction until these images superimpose 
(as in Fig.~3).  The number of divisions on the scale as viewed directly 
(by eye 2) which fall in one division of the image as seen through the 
telescope (by eye 1) is clearly the magnifying power of the telescope. \smallskip

\latex{\vspace*{-.05in}}Compare your measured magnification $M$ with that calculated  for an astronomical telescope,
namely $M= f_1/f_2$ where $f_1$ is the focal length of the objective and $f_2$ that of the eye 
piece.  Why are  the two different?  Calculate the magnification from the actual  
measured object
and image distances.  Compare with the measured $M$.}
\html{ & }
\latex{\parbox[s][0.in]{0.23\linewidth}}
{\hspace*{.0in}
\latex{\includegraphics[height=1.45in]{figs/l3-03.eps} }
\html{\begin{center} {\bf Figure~3:} \end{center}}
\html{\includegraphics[height=1.8in]{figs/l3-03.eps}}
\latex{\vspace*{-.12in}\begin{center} {~~~~Figure~3:} \end{center}}}
\html{ \cr \end{tabular}  }
\end{enumerate}

\item \latex{\vspace*{.25in}} {\em Erecting~telescope}
\setcounter{figure}{3}
\begin{figure}[!h] \centering
\latex{\vspace*{-.08in}}
\latex{\hspace*{.3in}\includegraphics[height=1.6in]{figs/l3-04.eps}}
\html{\includegraphics[height=2.0in]{figs/l3-04.eps}}
\latex{\vspace*{-.1in}}
\caption{Configuration of a three lens erecting telescope.}
\latex{\vspace*{-.05in}}
\end{figure}

\begin{enumerate}
\item[A.] \latex{\vspace*{-.2in}}Measure the focal length, $f$, of a second strong converging lens and use it as 
the inverting lens L$_3$ (Fig.~4) to form an erecting telescope.  L$_2$ must be adjusted
to give a real image, I$_2$. 
Notice that 
varying the space between 
I$_1$ and the inverting lens L$_3$ changes the magnification.
If you are using the web-based
lab manual and desire a demonstration, click on the Erecting Telescope Demo button 
immediately below.  In this simulation your are now able to readjust both the positions and
focal lengths!
%%%\input{toolbar/l03_j2}

\item[B.] \latex{\vspace*{-.06in}}What position of the inverting lens makes the shortest possible telescope, 
(i.e.~it makes the distance between I$_1$ and I$_2$ a minimum)?
\end{enumerate}
\item \latex{\vspace*{-.14in}}{\em Simple~microscope~or~magnifier}:
Experiment with one of the strong converging lenses as a magnifier until 
you can make the virtual image appear at any distance you choose:  vary 
the object distance from zero to the focal length.  The 
parallax test described in Part~1 will enable you to locate the virtual 
image. When the parallax between the object and the virtual image (seen 
through the lens) vanishes, the object and virtual image are in the same 
plane.

\item \latex{\vspace*{-.14in}}\html{\begin{tabular}{p{3.5in}l}}
\latex{\parbox[t][1.1in][s]{0.35\linewidth}}
{
{\em Compound~microscope:} Use the two strong converging lenses to form a compound microscope.
} 
\html{ & }
\latex{\parbox[s][0.in]{0.650\linewidth}}
{\hspace*{.03in}
\html{\begin{center} {\bf Figure~5:} Setup for compound microscope.\end{center}}
\html{\includegraphics[height=2.in]{figs/l3-05.eps}}
\latex{\includegraphics[height=1.55in]{figs/l3-05.eps}}
\latex{\vspace*{-.00in}\begin{center} {Figure~5:}  Setup for compound microscope. \end{center}}}
\html{ \cr \end{tabular}  }
\newpage

\item {\em Galilean~telescope~(or~opera~glass)}: Make use of the 
weak converging lens and a strong diverging lens.
\end{enumerate}
\noindent  {OPTIONAL}:
\begin{enumerate}
\item \latex{\vspace*{-.07in}}{\em Ramsden~eyepiece}
\begin{enumerate}
\item[A.] \latex{\vspace*{-.07in}}Ask the instructor for the holder containing a Ramsden eyepiece, a 
crosshair, a diaphragm, and an objective lens.  See Fig.~6.

\setcounter{figure}{5}
\begin{figure}[!hb] \centering
\latex{\vspace*{-.08in}}
\latex{\hspace*{.3in}\includegraphics[height=1.6in]{figs/l3-06.eps}}
\html{\includegraphics[height=1.8in]{figs/l3-06.eps}}
\latex{\vspace*{-.1in}}
\caption{Construction of a Ramsden eyepiece.}
\latex{\vspace*{-.1in}}\end{figure}

\noindent The Ramsden eyepiece consists of lenses 
1 and 2, plano-convex lenses of $f= 85$~mm.  Spherical aberration is 
less than for a single
lens because the ray bending is spread 
over four surfaces. It is a minimum if the curved surfaces face one 
another as shown.  (In addition if the two lenses were 
their focal length apart, chromatic aberration would be a minimum.  But, 
since dirt specks on lens 1 then would be in focus, lenses 1 and 2 are 
usually set $2f/3$ apart).  The tube also contains an objective lens to 
convert the tube into a telescope or microscope.  
\item[B.] Use the Ramsden eyepiece 
with $d=2f/3$ in the telescope and microscope.  
Note improvement in image over that of a single eyepiece lens.  
Adjust eyepiece for a sharp image of the cross hairs.  Then 
move the objective lens until the image shows no parallax 
with respect to the cross hairs.
\end{enumerate}
\item {\em Huygens eyepiece}:
A common eyepiece in which the image (and hence 
cross hair) is within the eyepiece.  It also employs two 
plano-convex lenses but both convex surfaces are toward the incident light.  
Minimum lateral chromatic aberration exists for a 
separation of ($f_1+f_2)/2$.  Usually $f_1 \sim 3f_2$.

\begin{figure}[!h] \centering
\latex{\vspace*{-.08in}}
\latex{\hspace*{.3in}\includegraphics[height=1.9in]{figs/l3-07.eps}}
\html{\includegraphics[height=2.2in]{figs/l3-07.eps}}
\latex{\vspace*{-.1in}}
\caption{Construction of a Huygens eyepiece.}
\end{figure}

\item {\em Eye~ring}.  
\begin{enumerate}
\item[A.] Point the astronomical telescope at a lamp and 
explore with a screen the illumination back of the eyepiece.  [Or remove 
diaphragm from telescope or microscope of optional (1)].

\begin{figure}[!h] \centering
\latex{\vspace*{-.08in}}
\latex{\hspace*{.3in}\includegraphics[height=1.2in]{figs/l3-08.eps}}
\html{\includegraphics[height=1.3in]{figs/l3-08.eps}}
\latex{\vspace*{-.1in}}
\caption{Position of eye ring.}
\end{figure}

\noindent The light coming through the telescope has a 
minimum cross section at ER.  This
area ER is the image of the objective formed by 
the eyepiece. Obviously all light which gets through the telescope 
must go through this image, and thus ER is the best spot to place the pupil 
of the eye. Hence the name ``eye ring''.

\noindent Note that if one places a diaphragm with aperture appropriately larger 
than the eye ring a little ahead of the eye ring, then an observer looking 
through the aperture would position the pupil of her/his eye on the eye 
ring.
\item[B.] Using the Ramsden eyepiece, place the diaphragm at 
the appropriate distance in 
front of the eye ring.  Note the improvement in the ease of observing 
through it, especially for the compound microscope.
\end{enumerate}
\item {OPTIONAL~telescope}: 
Use an achromatic objective lens, of long focal length and a commercial 
Ramsden eyepiece (from instructor).  Note the quality of the image.
\item {OPTIONAL~microscope}:
Use a short focal length achromatic objective 
and a commercial Ramsden eyepiece (from instructor).  Note the 
quality of the image.

\noindent It is interesting that one does not need an achromatic eyepiece because 
the virtual images for red and blue, though at different distances (e.g., red 
at 2~m, blue at $\sim \infty $), subtend almost the same angle at eye.  As a 
result the eye doesn't notice the aberration.
\end{enumerate}

