%\label{TravellingMicroscope}
\subsection{The Travelling  Microscope} 
\label{TravellingMicroscope}
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}} 
The sliding carriage of the traveling microscope rides on carefully machined ways, pushed by a nut under the carriage which rides on the micrometer screw.   The nut must not fit tightly on the screw or it will bind; hence there is always some slack built into the mechanism. 
\end{enumerate}

\hspace*{.1in}
\html{ \begin{tabular}{p{3.5in}l} }
\latex{\parbox{0.3\linewidth}}
{When the nut is being pulled to the right (dial being turned toward larger numbers), the screw threads will press against the threads in the nut as shown in Fig.~1, with the screw threads in contact with the back side of the threads on the nut.  When the direction of turning reverses, the screw threads then push on 
the front side of the nut threads.} 
\hspace*{.4in}
\html{ & }
\latex{\parbox{0.50\linewidth}}
{\hspace*{.5in}
\includegraphics[width=2.1in]{figs/a02-01.eps}
\begin{center} Figure~1: Backlash in screw mechanism.
\end{center}  }
\html{ \cr \end{tabular}  }

\latex{\medskip} 
\begin{enumerate}
\item[] For the microscope set initially on the same line for both directions of motion, the readings will differ by distance S, the backlash (slop) in the mechanism. \\

One way to avoid trouble with this slack is always to make settings after  turning the screw more than the slack in one direction, say the direction of increasing readings.  If one overshoots on a reading,  go back by more than the slack and then turn forward again.  The screw will then always press on the same side of the nut and no error arises. \\

A much better experimental technique is to take readings both ways.  Suppose one wants to measure the distance between two lines, 1 and 2.  Call  the reading turned toward larger readings on line 1, $D_{1}$ and when turning  in the reverse direction, $R_{1}$;  similarly for $D_{2}$ and $R_{2}$.  Then the  distance between the lines will be $D_{2}~-~D_{1}$ and also $R_{2}~-~R_{1}$ so that  one has immediately two independent readings to compare.  More important,  $D_{1}~-~R_{1}$ is the slack in the mechanism; it should equal $D_{2}~-~R_{2}$ and  should be the same for all pairs of readings.  If $D~-~R$ changes by more than  the experimental error in setting, you know immediately you have made a  blunder in either setting or reading and can immediately repeat the  measurement.  The constancy of D~-~R is actually an excellent measure of the  uncertainty in the measurements you are taking.
\end{enumerate}


\newpage

\subsection{The Optical Lever}

\begin{enumerate}
\item[]
An optical lever is a convenient device to magnify a small displacement and thus to make possible an accurate measurement of the displacement.  Experiment M-11, Young's modulus, uses an optical lever to magnify the  extension of a wire produced by a series of different loads. \smallskip 

%\html{ \begin{tabular}{p{3.5in}l} }
\latex{\parbox{0.3\linewidth}}
{The plate P carries a mirror M.  The mirror mount has two points resting in a fixed groove, F, and at the other end has a single point resting on the object whose displacement one is measuring.  Raising the object through a distance $\Delta L$ will tilt the mirror through an angle $\theta $ or $\Delta L/d$ radians (approximately) but will turn the light beam through an angle $2\theta $. \smallskip  } 
%\html{ & }
\latex{\parbox{0.70\linewidth}}
{
\latex{\includegraphics[width=4.5in]{figs/a03-01.eps}}
\html{\includegraphics[width=5.7in]{figs/a03-01.eps}}
\\   \begin{center} Figure~1: Schematic of the optical lever.
\end{center}  }
%\html{ \cr \end{tabular}  }

Hence
\[\theta \; = \; \frac{\Delta L}{d} \sim \frac{\frac{1}{2} 
( y_1-y_0)}{D}\]
if $\theta $ is small so that $\theta \sim \tan \theta $.  Therefore
\[2\theta  = \frac{2\Delta L}{d} = \frac{y_1-y_0}{D}, \; \mbox{and} \;
 \Delta l = (y_1-y_0)\left[ \frac{d}{2D}\right]~~.\]

Note that with the telescope nearly perpendicular to the scale at the beginning then $y_0$ is close to the telescope, and the difference between two elongations ($\Delta L_2~-\Delta L_1$) is very accurately given by \[\Delta L_2~-~\Delta L_1 = \frac{y_2~d}{2D} - \frac{y_1~d}{2D} = \frac{( y_2-y_1) d}{2D}\]
 
\noindent where $y_{i}$ is the scale reading.  This relation holds so long as $2\theta $ is small enough that $\tan 2\theta ~\sim ~2 \theta $.
\end{enumerate}
\newpage

\subsection{PARALLAX~and~Notes~on~using~a~Telescope}
\label{parallax}
\begin{enumerate}
\item {\em PARALLAX}:

To do quantitative work in optics one must understand {\em parallax} and how it  may be eliminated.  PARALLAX is defined as {\em apparent motion of an object  caused by actual motion of the observer}. \smallskip 

\html{ \begin{tabular}{p{2.5in}l} }
\latex{\parbox{0.55\linewidth}}
{When the observer's eye is in position 1, objects 1 and 2 are in line and may appear to coincide.  If the eye is moved to the left to position two, object 1 (i.e.~O$_1$) appears to move to the left with respect to object 2, (i.e.~O$_2$).
If the eye moves to the right to position 3, object 1 (O$_1$) appears to move to the right with respect to object 2 (O$_2$).  \smallskip}
\hspace*{.1in}
\html{ & }
\latex{\parbox{0.4\linewidth}}
{\hspace*{.2in}
\includegraphics[width=1.9in]{figs/a04-01.eps}
}
\html{ \\ \end{tabular}  }

As object 1 moves toward position 2 along the dotted line, its apparent displacement with respect to object 2 caused by motion of the eye from 2 to 3 gets smaller until it vanishes when O$_1$ and O$_2$ coincide. When O$_1$ gets closer to the eye than O$_2$, the direction of its apparent displacement reverses 
for the same eye motion.  In short, the object farthest from the eye apparently 
moves in the same direction as the eye.  Try this with two fingers.
\smallskip

Note that if O$_1$ is an image and O$_2$ a cross hair, the absence of parallax shows that the cross hairs are in the plane of the image.

\item {\em Focusing~a~Telescope~for~Parallel~Rays}:
\begin{figure}[!h] \centering
\includegraphics[height=1.1in]{figs/a04-02.eps}
\end{figure}

\vspace*{-.1in} The eyepiece E slides back and forth in the tube T and one should first adjust the eyepiece to give a clear image of the cross hairs.  Then move the tube T back and forth in the barrel B until the image of a distant object, formed by the objective O, falls on the plane of the cross hairs.  The test for this is the absence of parallax between the cross hairs and image.  

The rays from a distant object are nearly parallel.  For viewing a distant object, use an open window if the window glass is not accurately plane.  Otherwise poor image formation may result.  You can check by trying it both ways. At night use a distant object in the hallway.

The telescope, now focused for parallel rays, will stay so as long as the distance between O and C is unchanged.  One may still adjust the eyepiece position to suit the observer.

\item {\em Finding~an~Image~in~a~Telescope}:  

If you have trouble finding an image in a telescope, locate the image first with your unaided eye, and then pull the telescope in front of your eye, aligning it with your line of sight.  With high magnification it is difficult to find the image in the telescope because the alignment must be nearly perfect before the image appears in the field of view.  The eye has a rather large field of view so that the image will be visible over a range of positions.
\end{enumerate}

\newpage
\subsection{Notes~on~Radiation~Dosage,~Dosimetry,~and~the~Radon~Problem}
\noindent INTRODUCTION:
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}} 
The biological effects of radiation arise from the absorption of the radiant energy to produce heat, electronic excitation and/or ionization.\latex{\medskip}

Radio, T.V., microwave, visible light, u.v.~light, x-rays, $\gamma$-rays are 
all electromagnetic radiation and differ only in wavelength.  Electromagnetic radiation may have both beneficial and harmful effects:  e.g.~u.v.~light absorbed by the skin can supply needed vitamin D, but excess u.v.~radiation accounts for much skin cancer.  X-rays and $\gamma $-rays are more penetrating and so can 
affect tissue below the skin.\latex{\medskip}

Besides electromagnetic radiation one has high velocity charged  (and neutral) particles.  From {\em naturally} radioactive materials, the charged particles 
are either high speed electrons ($\beta$'s, beta rays) or alpha particles ($\alpha$'s, the nuclei of helium atoms).  Both types are rather easily stopped by a small thickness of matter e.g.~$\sim $ 1.8~mm Al stops 1.17 MeV $\beta $'s from RaE, and $\sim $~0.06 mm Al stops 5.3~Mev $\alpha $'s from Po. Hence natural radioactivities are normally of little concern unless the parent nucleus has been inhaled or ingested in the body.  The biological effects of neutral particles (e.g.~neutrons and neutrinos) from naturally radioactive materials are normally negligible.
%\end{mp1}

\begin{description}{}{}

\item[Radioactivity~unit:] 1 Becquerel~(Bq)~=~1~disintegration/s 
$\cong $~27~{pCi} (picoCurie)

\item[Radiation~dose] is the radiant energy absorbed per unit mass.

\item[~~~~Dose UNITS:] 0.01 J of radiation absorbed/kg of 
mass =~1~rad\\
\hspace*{1.1in} 1 J of radiation absorbed/kg of mass =~1~gray  (abbreviated {\bf Gy})

\item[~~~~Dose Equivalent:] includes the long term {\em relative 
biological 
effects of different types of radiation}. The original unit was the 
{\bf rem}  ({\bf r}ad {\bf e}quivalent {\bf m}an), 
but the now recommended S.I.~unit is the 
{\bf sievert} (abbreviated Sv) with:\\
\hspace*{1.5in}   1~Sv~=~100~rem~=~10$^5$~mrem\\
\hspace*{0.9in} and so:  1 mSv = 100 mrem
\end{description} \medskip

\end{enumerate}

\noindent {Federal laws on permissible doses are}:  
\begin{enumerate}
\item For workers, $<$~50 mSv/year for a whole body dose, 
but employer must follow the ALARA ({\bf A}s {\bf L}ow {\bf A}s {\bf R}esonably {\bf A}chievable) principle. For the hands alone, 750 mSv/yr are allowed.
\item For the general population $<$~5 mSv/yr whole body dose.
\end{enumerate}

\noindent RADIATION SOURCES:
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}}
Besides the sun's u.v.~radiation, the natural 
environment contributes an unavoidable dose equivalent to $\sim $~1.3~mSv/yr
plus a variable dose from inhaled radon which often is several times 
larger: see {\bf The Radon Problem} (below). {\bf Hence the average natural 
background radiation dose is $\sim $~3~mSv/yr}.
About .25 mSv/yr of this dose comes from internal radioactivities in the 
body (chiefly $^{40}$K which constitutes 0.0119\% of natural K and has 
T$_{1/2} \sim 10^{9}$ years).  The rest comes from external natural 
radioactivities in the earth (chiefly decay chains of uranium and thorium, 
T$_{1/2} \sim 4 \times 10^{9}$ years and T$_{1/2} \sim 10^{10}$ 
years) and from 
cosmic rays.   The cosmic ray contribution increases with altitude and is
$\sim$ 30 mSv/yr at 40,000 feet elevation (jet airplane altitudes).\latex{\medskip}

 Brick and stone houses often have larger backgrounds.  Living in Denver
(elevation 5200 ft.) contributes an additional  $\sim $ 0.7 mSv/yr.  In the
Kerala region of India and the Espirito Santo region of  Brazil, natural
sources give $\sim $ 30 mSv/yr with no obvious  abnormality resulting to the
indigenous population so the Federal  regulations seem very conservative for
the general population.\latex{\medskip}

 Man-made radiation exposure averages $\sim $ .7 mSv/yr and  comes almost 
exclusively from medical and dental x-rays.  A single dental x-ray may 
involve 7~mSv to the skin.  Exposures from nuclear power generating 
stations are nearly zero.  In fact, per KWH of electricity generated, the 
radioactivity released from coal fired plants is often high compared to
that  permitted from nuclear plants since many coals contain appreciable
uranium  and/or thorium plus the equilibrium decay products from these
long-lived  radioactive nuclei.\latex{\medskip}

For perspective on radiation exposure, Prof.~Cameron formerly of the UW 
Medical Physics Dept.~suggests translating doses into a natural unit, the
{\bf BERT} defined as the {\bf B}ackground {\bf E}quivalent {\bf R}adiation 
{\bf T}ime.   Thus a {\bf BERT equal to 1 yr would correspond to 3~mSv} (see above discussion on average background dose).\latex{\medskip}
\end{enumerate}

\noindent THE RADON PROBLEM:
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}}
Radon (an inert gas) from decay of naturally occurring U and Th in the earth continually diffuses into  the atmosphere and may cause $\sim $~10,000 lung cancer cases per year in the U.S.\  The radon content of outdoor air 1 meter above ground typically gives 4 to 15 becquerels/m$^3$ The health effects come mainly from inhalation of $^{222}$Rn (from U)since this radon isotope has a T$_{1/2}$ of 3.82 days whereas the thorium radon isotope ($^{220}$Rn) has T$_{1/2}$ of only 56 seconds.  The indoor air concentration of radon ($\sim $~50~Bq/m$^3$)  varies perhaps a factor of a thousand from location to location,
depending upon the U content and physical characteristics of the soil, 
moisture content, building construction, winds, etc.  (A house in Maine had a record $\sim $~160,000~Bq/m$^3$!)\latex{\medskip}

A radon concentration of 50~Bq/m$^3$ may result in an annual dose equivalent to bronchial epithelium (site of most radiation induced lung cancer) of $\sim $~2.5~mSv/yr.  Perhaps 25\% of Wisconsin houses have concentrations $>$~150~Bq/m$^3$ which is  the EPA guideline where action should be taken in a few years since the lung cancer risk may be comparable to smoking 3 to 10 cigarettes/day.  (M.S.~Blumenthal, {\bf Wisconsin Medical Journal}, Vol.~87, May 1988, p.17) In fact 2\% of U.S.~homes have radon concentrations $>$~300~Bq/m$^3$ and occupants should take action to reduce the concentration since they 
may be receiving an effective dose of $> \sim $~16~mSv/yr.  (By contrast the 
EPA limit for off-site exposure from nuclear reactors or from nuclear waste 
depositories is only .25~mSv/yr!)  (Bodansky, {\bf Physics and Society} 16, No.~4, p.~6, 1987).\latex{\medskip}

If a house has high radon levels, then the radon ingress usually is from air infiltration from soil beneath the house.  Natural convection in the house (chimney effect) tends to pull in the radon contaminated air.  A 
solution is to drive pipes through the basement floor and connect them to fans exhausting to the outside air.  See A. V. Nero Jr. ``The Indoor Radon Story'', {\bf Technology Review} Vol.89, No.~1, p.~28, (1986); also A. Nero, ``Earth, Air, Radon and Home'', {\bf Physics Today}, Vol 42, No. 4, p.32, (1989).\latex{\medskip}

A good general reference on the subject is 
{\bf ``Radon and its Decay Products in Indoor Air''} edited by William Nazaroff and A.V.~Nero, Jr., John Wiley \& Sons, 1988.  Ground water supplies often contain high concentrations of radon from uranium decay in the aquifers.  The radon concentration in public ground water supplies averages $\sim $~5000~Bq/m$^3$, and is much higher in some of the New England states.  The health hazard is apparently not from drinking the water, but from the water's contribution to the indoor radon air problem: perhaps $\sim $~5~Bq/m$^3$.  Private wells often have high concentrations.  Storage or aeration of the water provides effective control of the hazard.
\end{enumerate}

\noindent OTHER ISSUES:
\begin{enumerate}
\item[] \latex{\vspace*{-.05in}}
\begin{center}
{\bf Is a Small Amount of Radiation Healthy - The Hormesis Effect}
\end{center}

The following is from RADIATION DOSIMETRY by former Prof.~John R.~Cameron, 
Department of Medical Physics, UW, Madison:
\begin{quote}
``Studies on nuclear workers often show that they have less cancer than other member of the population and even of other workers with similar jobs. This is usually explained as the 'healthy worker' effect.  That is, for reasons not understood, radiation work attract healthy workers.  An alternate explanation which is rarely mentioned is the possibility that a small amount of radiation is good for you.  This is referred to as the 'hormesis' effect.  Since humans and all of our ancestors evolved in a sea of natural radiation, it is possible that mutations have occurred that produce the hormesis effect.  Animal experiments have demonstrated the hormesis effect.  Rats exposed to increased radiation have a longer survival than their controls.''
\end{quote}
\end{enumerate}


