\section{Introduction}

Unlike other scientists, astronomers are far away from the objects
they want to examine.  Therefore astronomers learn everything about an
object by studying the light it emits.  Since objects of astronomical
interest are far away, they appear very dim and small to us.  Thus
astronomers must depend upon telescopes to gather more information.
Lenses and mirrors are used in telescopes which are the only instruments
astronomers can use to look at celestial objects.  Therefore it is
important for us to have a basic understanding of optics in order to
optimize telescopes and interpret the information we receive from
them.

The basic idea of optics is that mirrors or lenses can be used to
change the direction which light travels.  Mirrors change the
direction of light by \textit{reflecting} the light, while lenses redirect
light by \textit{refracting}, or bending the light.  

The theory of optics is an important part of astronomy, but it is also
very useful in other fields.  Biologists use microscopes with multiple
lenses to see very small objects.  People in the telecommunications
field use fiber optic cables to carry information at the speed of
light.  Many people benefit from optics by having their vision
corrected with eyeglasses or contact lenses.  

This lab will teach you some of the basic principles of optics which
will allow you to be able to predict what mirrors and lenses will do to
the light which is incident on them.  In the following lab, we will deal
with the actual telescope instruments and camera devices, so the basic
skills you learn in this lab will help you understand telescopes better.

\begin{itemize}
\item{{\it Goals:}  to discuss the properties of mirrors and lenses, and demonstrate them using an optics kit and worksheet}
\item{{\it Materials:}  optics kit, ray trace worksheet, ruler}
\end{itemize}

\section{Discussion}

The behavior of light depends on how it strikes the surface of an
object.  All angles are measured with respect to the {\bf normal} direction.
The normal direction is defined as a line which is perpendicular to
the surface of the object.  The angle between the normal direction and
the surface of the object is $90^{\circ}$.  Some important definitions
are given below.  Pay special attention to the pictures in Figure 
\ref{fig:optics}
since they relate to the reflective (mirrors) and refractive (lenses)
optics which will be discussed in this lab.
        
\begin{figure}[h]
\centering
\leavevmode
\epsfxsize=1.05\textwidth
\epsfbox{OPTICS/Optics_fig1.eps}
\caption{}
\label{fig:optics}
\end{figure}
 
\begin{itemize}
\item{{\bf n} = line which is always perpendicular to the surface; 
also called the {\it normal}}
\item{{\bf $\theta$$_I$} = angle of {\it incidence}; the angle between the {\it incoming} 
light ray and the normal to the surface}
\item{{\bf $\theta$$_R$} = angle of {\it reflection}; the angle between the 
{\it outgoing} light ray and the normal to the surface}
\item{{\bf $\alpha$$_R$} = angle of {\it refraction}; the angle between the 
{\it transmitted} light ray and the normal direction}
\end{itemize}

\subsection{Reflective Optics: Mirrors}

How do mirrors work? Let's experiment by reflecting light off of a simple
flat mirror.

In small groups, set up the simple optics kits, which contain a
light source, a white tray with slits, a white slit mask, two
mirrors, three lenses, and a protractor.  If not already done, slide the
light bulb as far back as it will go (i.e. slide the silver screw on
top of the grey box to the back of the slit).  In addition, always
keep the light source against the slitted front of the white tray. 

Place the white metal mask between the light source
and the front of the slitted white tray, so that only one beam of
light is emitted.  Line up the slits at the front of the tray with the
arrows on the worksheet.  Insert the plane mirror upright into the
protractor, and place this in the designated position on the
worksheet.  Make a dark point at the origin of the protractor and
some dark marks every 10 degrees, so you will be able to measure the
angles and point the light source correctly even after the room lights
are turned off (which they will need to be for you to see the light rays).
Turn the light source on, and trace the incident and
reflected light rays (Do your best drawing under the protractor).
Measure the angles of incidence and reflection and write the values
below.  

\smallspace

Now experiment using different angles of incidence by rotating the protractor.
Make a small table of angle of incidence vs. angle of reflection.
\textit{(5 points)}

\smallspace

What do you conclude about how light is reflected from a mirror?

\smallspace

The law governing the behavior of light when it strikes a mirror is
known as the {\bf Law of Reflection}:

\begin{center}
angle of incidence = angle of reflection \\
$\theta$$_I$ = $\theta$$_R$  
\end{center}

OK, now what happens if you make the mirror curved? First let's consider
a \textit{concave} mirror, one which is curved \textit{towards} the
light source.  Try to think about the curved mirror as being made up of
lots of small sections of flat mirrors, and make a prediction for what
you will see if you put a curved mirror in the light path. You might
try to make a drawing.

\smallspace

Take out the white mask so that light is coming from all three slits.
Put the curved mirror in the light path (you might find it easier to
use the worksheet and place the mirror at the specified location) and trace 
the light rays.  Draw a diagram to show what you got.
\textit{(5 points)}

\smallspace

Now make a prediction for what you will see for a \textit{convex} mirror,
one which is curved \textit{away} from the light source.

\smallspace

Now put the convex mirror (just use the other side of the concave mirror)
in the light path (you might find it easier to use the worksheet and
place the mirror at the specified location and trace the light rays.
Draw a diagram to show what you got.  \textit{(5 points)}

\smallspace

Now go back and put the flat mirror in the light path using light from
all three slits. Note the separation of the 3 reflected beams and compare
this with the reflected beams from the concave and convex mirrors. What
do you find?  \textit{(5 points)}

\smallspace

From these experiments, we can draw the conclusion that \textit{concave
mirrors focus light, convex mirrors diverge light.}

\subsection{Refractive Optics: Lenses}

OK, how about lenses? Do they work in a similar way?

Place the concave and convex lenses on the worksheet and trace the
rays. How do concave and convex lenses affect the path of the light?
\textit{(5 points)}

\smallspace

How does the behavior of lenses compare with the behavior of mirrors?
Note some similarities and differences.  \textit{(5 points)}

\smallspace

\subsection{Convergence of light: focal length}

Using the concave mirror and the convex lens, get a rough estimate of
the distance from the mirror or lens to the place where the light rays
come together. Note that since the lens is part of a sphere, the light
rays from the lens will actually focus at or slightly below the level of
the table, so you may need to put the light source at the edge of a table
to find the location where the light rays converge.  \textit{(5 points)}

Distance from concave mirror to convergence point: \blank

Distance from convex lens to convergence point: \blank

This distance is called the \textit{focal length} of the optic.

\subsection{What can optics do for you?}

Write down a list of different objects in your everyday experience which
use optics.  \textit{(5 points)}

\smallspace

Consider a camera, binoculars, microscope, and telescope. What is the
function of optics in each of these objects?  \textit{(5 points)}

\smallspace

\subsubsection{Making Images}

One important function of optics is to make images of things. In fact,
your eyes contain objects which make images which allow us to see
things! This is also what a camera does.

To make an image, optics take all of the light which comes from an object
and concentrates it all in one place. Considering your experiments with
mirrors and lenses above, which shape of mirror and which shape of lens
makes the light converge?  \textit{(5 points)}

\smallspace

To demonstrate how images are made, look at some object outside the
window.  Hold up a white piece of paper towards the object. Note that you
cannot see the object on the paper! Now place the convex lens in front of
the paper; you should locate it about one focal length (measured above)
in front of the paper. Can you see the image of your object?

\subsubsection{Magnifying/Demagnifying}

Another function of optics is to magnify or demagnify things, that is,
to make them appear larger or smaller. Use your concave and convex lenses
to look at nearby objects (for example, the table top, or the lab manual,
etc.)  and see how magnification works. Experiment with placing the lens
near to the object you want to look at and then move it farther away.

First try the convex lens. Does it magnify or demagnify? How does
the magnification depend on the distance of the lens from the object?
\textit{(5 points)}

\smallspace

Next try the concave lens. Does it magnify or demagnify? How does the
magnification depend on the distance of the lense from the object?
\textit{(5 points)}

\smallspace

Note that the behavior of magnification can get a bit complicated: it
can change depending on both the location of the lens from the object
and also your eye from the lens. However, the behavior of a lens and
its magnification actually follows a relativley simple mathematical
behavior. We won't go into it here, but ask your instructor if you are
curious about learning more.

\subsubsection{Collecting Light}

Finally we come to the main function of optics in astronomical telescopes,
namely, to collect light. When optics are used to make images, light
coming to different locations is all focussed to a single location.
As a result, if you use a bigger optical element, you can collect
more light into your image, and, as a result, make the image appear
\textit{brighter}. This is the main function of telescopes: to make
faint objects appear brighter, and is the reason why telescope optics
are so big. Astronomical objects are faint, so to collect enough light,
we collect light which is going to fall over a wide area and concentrate
it all in a certain point.

To demonstrate this, use your convex lens to look at the outdoor object
again. Now use a piece of paper to cover up a portion of the lens.
How does the appearance of your image change as different
portions of the lens are covered?  \textit{(5 points)}

\smallspace

\section{Summary} 

({\it 35 points}) Please summarize the important concepts of this
lab.

\begin{itemize}
\item{Describe the properties of the different types of lenses $and$
mirrors discussed in this lab}
\item{What are some of the differences between mirrors and lenses?}
\item{Why is the study of optics important in astronomy?}  
\end{itemize}

\noindent
Use complete sentences, and proofread your lab before handing it in.
\clearpage
\begin{figure}[h]
\centering
\leavevmode
\epsfxsize=1.05\textwidth
\epsfbox{OPTICS/lensfig1.eps}
\caption{Worksheet for section 8.2.1}
\end{figure}
\clearpage
\begin{figure}[h]
\centering
\leavevmode
\epsfxsize=1.05\textwidth
\epsfbox{OPTICS/lensfig2.eps}
\caption{}
\end{figure}
  
%\end{document}
