Physical Optics: Refraction
last updated August 6, 2003
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(Explanatory Note:  This lab is shortened from its original version to accomidate the shortness of the summer term.  If you are interested in the original lab notes, then you may find them at http://www2.hawaii.edu/~jmcfatri/labs/refraction.html
P re-lab:
None, but you might want to check out http://www.colorado.edu/physics/2000/quantumzone/  (this might take a moment to load, because there are applets on the page).
Objectives
The goals of this lab are to:
N otes on Chapter 13
pp 93 - 101 of your lab book
In today's experiment, we will be using a simple spectrometer to find the wavelengths of light that characterize the sodium doublet lines. A spectrometer is a very important device in many sciences! Astronomers use spectrometry to determine the composition of stars and planets.  Biologists and chemists use spectrometry to determine the atomic composition of unknown materials. In physics, spectrometry helps us understand the structure of atoms.  Simply put, a spectrometer is a device which separates and measures the wavelengths of light which are emitted from a light source.

As you learned in Chemistry, every atom emits a unique "signature" spectrum. That is, every atom has a set of very specific wavelengths which it emits.  Atoms behave in this way because each atom has a unique set of energy levels it can exist at.  In Chemistry, you called these levels "s", "p", "d", etc.  (Actually, this "s" and "p" notation comes from spectrometry. They come from the words "sharp", "principal", "diffuse", and "fundamental", which scientists were using before they understood the structure of atoms! The words describe how the spectral lines looked in a spectrometer.)  In our lab, we would like to find the wavelength of light which is emitted when the atom goes from the 3p energy state to the 3s energy state for the sodium atom.

(Side note: actually, saying "the" 3p energy level is wrong. The 3p energy level is split into two levels due to the spin-orbit effect, so in real life there are two spectral lines observed, one from the a slightly higher energy 3p level, and one from a slightly lower 3p level. This line structure is known as fine-structure splitting. Our instrument is not sensitive enough to observe this effect, however, so we will ignore the fact that there are two lines from 3p to 3s.)

The spectrometers we are using in this lab are very old; they are, in fact, antiques! However, this spectrometer has many advantages over newer spectrometers, the main one being pedagogical. Unlike newer devices, this spectrometer uses a very simple and familiar device to separate and measure wavelengths: a prism. You know that if you shine white light through a prism you will see a rainbow come out of the other side. This occurs because of dispersion: the index of refraction of a material changes for different wavelengths.  

The index of refraction tells you how much bending of the ray will occur.  We can figure the amount of bending quantitatively by Snell's Law:

n1* sin(theta1) = n2 * sin(theta2)

where n1 and n2 are indicies of refraction,
theta1 and theta2 are the angles the light ray makes to the normal of the interface surface.

Since the index of refraction is different for each wavelength, each color will be bent differently through the prism. (Red gets bent the least and violet light gets bent the most). By measuring the amount of bending our light ray experiences, we can then figure out the wavelength.

Of course, before we can do this, we have to know what kind of glass our prism is made out of. That will tell us how much bending will occur for each wavelength.

To find what kind of glass our prism is made of, we will use the argument given on pp. 93 - 94 of your lab manual (based on Snell's law and geometry), which yields:
 
n/n' = sin (1/2 (D_min + alpha))/ sin (1/2* alpha)      (1)

We will discuss what each of these terms mean in class.  This equation reduces further when you consider n' is the index of refraction of air, which is 1, and alpha, the angle of our prism, is 60 degrees:
n = 2 sin(1/2 (D_min + 60))                    (2)

We will measure the index of refraction for known wavelengths using this formula.  The known wavelengths will be supplied by a mercurcy lamp; the specific wavelengths which the mercury atoms emit are given in the table on pg. 96. We know that the index of refraction can be represented by the series:
n= C0 + C2/ lambda ^2 + C4 /lambda ^4 + ...

Can you find C0, C2, and C4? If you can, then you can compare the index of refraction you get from this formula to the index of refraction for different materials given by the table on pg. 85 (which is copied from the Handbook of Chemistry and Physics)

Then, you can calibrate the spectrometer using mercury, and then compare to the bending you get from our unknown Sodium doublet line.
Procedure:
    Part I: Hg (Mercury) Lamp

    The apparatus:

    1. Pick a spectral line.  Keep the telescope crosshair on that line.
    2. The lines will move if you rotate the prism table.  Rotate the table such that the lines move right. (Move the telescope also so that you keep the crosshair on the line.)
    3. Move the line as far right as you can get it (keeping the crosshair on the line), record the angle on the vernier scale.  This is the D_min.
    4. Calculate the value of n, from equation 2 above.
    5. Repeat steps 1-4 for all 8 colored lines.
    6. Make a graph of the index of refraction, n, vs. 1/wavelength^2


    Part II: Determining the wavelengths of Na (Sodium) Lamp

    1. Using the procedure from part I, find the D_min of the green line (of the Hg lamp).
    2. Now lock the prism table so that it cannot move.
    3. Rotate the telescope until the crosshair is on the red line.  Record the angle on the vernier scale.  This is the angle theta, which will be close to, but not equal, the D_min.
    4. Repeat step 3 for all of the 8 lines (in order, starting from red).
    5. Replace the Hg lamp with the Na lamp (the orange colored one).  (DO NOT TOUCH THE PRISM!) Record the angle at which you find the yellow line.  
    6. Make a graph of theta vs. wavelength.  Manually draw a curve on your graph which best fits the line.  Determine the approximate wavelength of the sodium doublet by locating the point on the line with the angle you measured in step 5.
Data:
Part 1: Finding the glass type of the prism
wavelengths of mercury
(Angstroms)
 1/(wavelength)2
(       )
Minimum Deflection, D_min

 index
of
refraction
(use equation 2)
Degrees

Minutes

Minimum Deflection
D_min = Degrees + minutes/60
4046 (violet)




4078 (violet)




4358 (blue)




4916 (blue-green)




5461 (green)




5770 (yellow-orange)




5790 (yellow-orange)




6908 (red)





From the plot of the index of refraction, n, vs. 1/wavelength^2,
C0 = _____________+/- ____________
C2 = _____________+/-_____________

Show your usual sample equations below:














What type of glass do you have? To figure this out, calculate the index of refraction for the wavelengths 4340 A, 4860 A, 5890 A, and 6560 A.  Show your work below.











Compare your values with the ones in Table 12.1 on pg. 85.

Your glass type is:___________________

Part 2: Calibrating the spectrometer
wavelengths of mercury
(Angstroms)
 angle at which you see the line
4046 (violet)
4078 (violet)
4358 (blue)
4916 (blue-green)
5461 (green)
5770 (yellow-orange)
5790 (yellow-orange)
6908 (red)

the angle of the sodium doublet line (yellow-orange): __________________+/- ________________
From your plot of wavelength versus angle, the wavelength of the sodium doublet line is: ______________+/- ______________
Assignment:
Write a one paragraph conclusion below: