\section{Introduction}


For many celestial objects, light is the astronomer's only subject for
study. Light from celestial objects is packed with amazingly large
amounts of information. Studying the distribution of brightness for each
wavelength (color) which makes up the light provides the temperature of a
source. A simple example of this comes from flame color comparison. Think
of the color of a flame from a candle (yellow) and a flame from a
chemistry class Bunson burner (blue). Which is hotter? The flame from
the Bunson burner is hotter. By observing which color is dominant in
the flame, we can determine which flame is hotter or cooler.  The same
is true for stars; by observing the color of stars, we can determine
which stars are hotter than the others.

In this lab, you will study a basic form of light from celestial objects
called \textit{blackbody radiation}.  The study of this radiation will
provide you with an understanding of just how much information may be
derived from a very simple observation.

This lab is split into two parts: 
\begin{itemize}
\item Experimentation with actual light sources to learn about the 
qualitative behavior of blackbody radiation
\item Experimentation with computer simulations of blackbody radiation to
learn about the quantitative behavior of blackbody radiation
\end{itemize}

The two stations can be performed in either order, so half the groups can
work on the computers while the other half works with spectrographs, and 
then the groups can switch places.

\begin{itemize}
\item{{\it Goals:} to discuss the properties of blackbody radiation, filters, 
and see the relationship between temperature and color by observing light 
bulbs through a spectrograph, and using a computer simulation of blackbody
radiation}
\item{{\it Materials:} spectrograph, adjustable light source, gas tubes and
power source, computers, calculators}
\end{itemize}

\section{Discussion}

{\it Blackbody radiation (light) is produced by any hot, dense object.}
By ``hot'' we mean any object with a temperature above absolute zero.
All things in the Universe emit radiation, since all things in the
Universe have temperatures above absolute zero.   Astronomers {\it
idealize} a perfect absorber and perfect emitter of radiation and call it
a ``blackbody''.  This does not mean it is black in color, simply that it
absorbs and emits light at all wavelengths, so no light is reflected.
A blackbody is an object which is a perfect absorber (absorbs at all
wavelengths) and a perfect emitter (emits at all wavelengths) and does
not reflect any light from its surface. Astronomical objects are not
perfect blackbodies, but some, in particular, stars, are fairly well
approximated by blackbodies.

The light emitted by a blackbody object is called blackbody radiation.
This radiation is characterized simply by the $temperature$ of the
blackbody object.  Thus, if we can study the blackbody radiation from
an object, we can determine the temperature of the object.

To study light, astronomers often split the light up into a spectrum.
A spectrum shows the distribution of brightness at many different
wavelengths.  Thus, a spectrum can be shown using a graph of brightness
vs. wavelength.  A simple example of this is if you were to look at a
rainbow and record how bright each of the separate colors were.  Figure
\ref{fig:rainbow} shows what the brightness of the colors in a rainbow
might look like.  At each separate color, a brightness is measured.
Viewed in this way, the rainbow is a spectrum of the light from the Sun.

\begin{figure}[h] 
\centering 
\leavevmode 
\epsfxsize=0.9\textwidth
\epsfbox{BLACKBODY/bb_fig1.eps} 
\caption{} 
\label{fig:rainbow}
\end{figure}

Light which has been split up to create a spectrum is called dispersed
light.  By dispersing light, one can see how pure white light is really
made up of all possible colors.  If we disperse light from astronomical
sources, we can learn a lot about that object.  To split up the light
so you can see the spectrum, one has to have some kind of tool which
disperses the light.  In the case of the rainbow mentioned above, the
dispersing element is actually the raindrops which are in the sky. Another
common dispersing element is a prism.

We will be using an optical element called a {\it diffraction grating} to
split a source of white light into its component colors.  A diffraction
grating is a bunch of really really small rectangular openings called
slits packed in close together on a single sheet of material, usually
plastic or glass.  They are usually made by first etching a piece of
glass with a diamond and a computer driven etching matchine and then
taking either casts of the original or a picture of the original.

The diffraction grating we will be using is located at the optical
entrance of an instrument called a $spectroscope$.  The image screen
inside the spectroscope is where the dispersed light ends up.  Instead of
having all the colors land on the same spot, they are dispersed across
the screen when the light is split up into its component wavelengths.
The resultant dispersed light image is called a spectrum.

\section{Observing light sources with a spectrograph}

In this section of the lab, we will study a common blackbody in
everyday use:  a simple white light bulb.  Your Lab TA
will show you a regular light bulb at two different brightnesses (which
correspond to two different temperatures).  The light bulb emits at all
wavelengths, even ones that we can't see with our human eyes.  

\begin{enumerate}
\item{First, get a spectroscope from your lab instructor.  Study 
Figure \ref{fig:spectrograph}
figure out which way the entrance slit
should line up with the light source.  {\bf DO NOT TOUCH THE ENTRANCE
SLIT OR DIFFRACTION GRATING!}   Touching the plastic ends degrades the
effectiveness and quality of the spectroscope.}
  
\begin{figure}[h]
\centering
\leavevmode
\epsfxsize=0.9\textwidth
\epsfbox{BLACKBODY/bb_fig2.eps}
\caption{}
\label{fig:spectrograph}
\end{figure}

\item Observe the light source at the brighter (hotter) setting. 

\item Do you see light at all different wavelengths/colors or only a
few discrete wavelengths? (\textit{5 points})
\smallspace

\item Of all of the colors which you see in the spectrographs, which color
appears the brightest?(\textit{5 points})
\smallspace

\item Observe the light source at the fainter (cooler) setting. 

\item Do you see light at all different wavelengths/colors or only a
few discrete wavelengths? 
Of all of the colors which you see in the spectrographs, which color
appears the brightest?
(\textit{5 points})
\smallspace

\item Describe the changes between the two light bulb observations. What
happened to the spectrum as the brightness and temperature of the
light bulb increased?  Specifically, what happened to the relative amount
of light at different wavelengths?(\textit{10 points})

\smallspace

\item Betelguese is a Red Giant Star found in the constellation
Orion. Sirius, the brightest star in the sky, is much hotter and
brighter than Betelguese. Describe how you might expect the colors of these 
two stars to differ. (\textit{10 points})

\smallspace

\item To get a feeling for a completely different type of spectrum,
use your spectrograph to look at the light from the tube containing
hot hydrogen gas. What kind of spectrum does this produce?

\smallspace

\end{enumerate}

\section{Quantitative behavior of blackbody radiation}

In this section, which should be done outside of class on a computer with
network access, we will investigate how changing the temperature of
a source changes the characteristics of the radiation which is emitted
by the source. We will see how the measurement of the \textit{color}
of an object can be used to determine the object's temperature. We
will also see how changing the temperature of a source also affects
the source's \textit{brightness}.

To do this, we will use an online computer program which simulates the
spectrum for objects at a given temperature. This 
program is located here:
http://www.mhhe.com/physsci/astronomy/applets/Blackbody/applet_files/BlackBody.html

The program just produces a graph 
of wavelength on the x-axis vs. brightness on the y-axis; you are
looking at the relative brightness of this source at different wavelengths.

The program is simple to use. There is a sliding bar on the bottom of the
``applet'' that allows you to set the temperature of the star.  Play around
with it a bit to get the idea. Be aware that the y-axis scale of the plot will
change to make sure that none of the spectrum goes off the top of the
plot; thus if you are looking at objects of different temperature,
the y-scale can be different.

Note that the temperature of the objects are measured in units called
degrees Kelvin (K). These are very similar to degrees Centigrade/Celsius (C);
the only difference is that: $K = C + 273$. So if the outdoor temperature
is about 20 C (68 Fahrenheit), then it is 293 K. Temperatures of stars
are measured in \textit{thousands} of degrees Kelvin; they are much hotter than
it is on Earth!

\begin{enumerate}
\item Set the object to a temperature of around 6000 degrees, which is
the temperature of the Sun. Note the wavelength, and the color of the spectrum
at the peak of the blackbody curve. 

\item Now set the temperature to 3000 K, much cooler than the Sun. 
How do the spectra differ? Consider both the \textit{relative}
amount of light at different wavelengths as well as the overall 
\textit{brightness}. Now set the temperature to 12,000 J, hotter than Sun. 
How do the spectra differ?  (\textit{5 points})

\smallspace

\item You can see that each blackbody spectrum has a wavelength where the
emission is the brightest (the ``top'' of the curve). Note that this wavelength
changes as the temperature is changed. Fill in the following small
table of the wavelength (in ``nanometers'') of the peak of the curve for 
objects of several different temperatures. You should read the wavelengths at
the peak of the curve by looking at the x-axis value of the peak.
(\textit{5 points})

\begin{table}[h]
\begin{center}
\bigskip
\begin{tabular}{c|c}
\hline
Temperature & Peak Wavelength  \\
\hline
\hline
3000  &  \\
6000  &  \\
12000  &  \\
24000  &  \\
\hline
\end{tabular}
\end{center}
\end{table}

\item Can you see a pattern from your table? For example, consider how the
peak wavelength changes as the temperature increases by a factor of 2, a
factor of 3, a factor of 4, etc. Can you come up with a mathematical expression
which relates the peak wavelength to the temperature?(\textit{5 points})

\smallspace

\item Where do you think the peak wavelength would be for objects on
Earth, at a temperature of about 300 degrees K?(\textit{5 points})

\smallspace

\item The color of a source is a measure of the \textit{relative} amount
of light at different wavelengths. If a source produces more red light
than blue light, it appears red; if it produces more blue light than
red light it appears blue. Astronomers measure the color by comparing the
amount of light in two different wavelength ranges, such as ``blue'' (450 nm)
and ``red'' (700 nm). For following exercise, you will be given a set of 
temperatures in the table, read off the value of the y-axis of the graphed
curve at both 450 and 700 nm, and then divide the two numbers.

Fill in the table for the relative amount of blue to red light (which is
just the blue brightness divided by the red brightness).(\textit{5 points})

\begin{table}[h]
\begin{center}
\bigskip
\begin{tabular}{l|l}
\hline
Temperature & Color = Blue / Red  \\
\hline
\hline
4000  &  \\
6000  &  \\
12000  &  \\
\hline
\end{tabular}
\end{center}
\end{table}

What can you say about this quantitative measurement of color as 
a function of temperature? Speculate on why it might be easier to make
this measurement of color than it is to look for the peak of the
curve (hint: think about how much light is collected over a range
of wavelengths as opposed to the amount collected at a single wavelength). 
(\textit{5 points})

\smallspace

\end{enumerate}

\section{Summary}

({\it 35 points})  Summarize the important ideas covered in this lab.
Some questions to answer are:

\begin{itemize}
\item{What information you can learn about a celestial object just
by measuring the peak of its blackbody spectrum?} 
\item{What  does a
blackbody spectrum look like?} 
\item{How does the peak wavelength change
as the temperature of a blackbody changes?} 
\item{How can you \textit{quantitatively} measure the color of an object?}
\item{Do the color of items you see around you on Earth (e.g. a red and
blue shirt) tell you something about the temperature of the object? Why
or why not?}
\end{itemize}

\noindent
Use complete sentences, and proofread your summary before handing in the lab.

%\end{document}



