L-6 SPECTROMETER

Instructor's Notes

This experiment can be performed in one three hour lab period if part (1) of Experiment A is done by the instructor before class, and the students are instructed (by a demonstration) how to perform the prism table leveling.

EQUIPMENT SET-UP AND MAINTENANCE CHECKLIST

  • Gaertner-Peck Spectrometer
  • Cloth dust cover/light shield for spectrometer.
  • Gauss eyepiece and illuminator, with power supply.
  • Equilateral glass prism, or right angle prism.
  • Spectrum tube power supply, with 3800 ohm rheostat if needed.
  • Spectrum tubes (Geissler tubes): Mercury, Helium, Argon, etc.
  • Desk lamp, or other low intensity white light source.
  • Holder or padded tray for the prism table when it is removed from the spectrometer.

1. See that the Gauss eyepiece illuminator is well lined-up with the hole in the eyepiece wall, for brightest crosshair image. Do this by removing the eyelens assembly (with illuminator attached) from the telescope tube. Then look into it backwards (at the light emerging, which would normally go toward the telescope objective). Look at an angle slightly downward, to see if the round hole seems uniformly illuminated with a brighter spot at its center. If the bright spot is not centered, loosen the two screws and carefully rotate the eyelens with respect to the illuminator until the brightest spot is centered in the hole. Sometimes it may help to rotate the bulb socket at the bottom of the illuminator, if the bulb is skewed, as so many cheaply-produced bulbs are these days.

2. Clean the prisms with lens tissue moistened with alcohol, to remove fingerprints.

3. Check for free and smooth motion of the prism table. If the instrument has not been used for a while the lubricant on the shaft has "set." Wipe off the old lubricant with an oil-soaked cloth, then re-apply lubricant with a clean oil-dampened cloth. [An oily finger works, also.] In extreme cases a solvent-lubricant may be necessary to remove the old, hardened, lubricant. WD-40 is good for this. But it is not the best lubricant, so wipe it off after cleaning and apply a good quality camera oil, or silicon oil.

4. Clean dust from the entire instrument. Clean dust and grit from the surface of the main scale.

5. Check the collimation of the telescope, using the Gauss eyepiece and illuminator. Adjust if necessary.

6. Parallax between slit and cross hairs must be eliminated to ensure that light from any point of the slit emerges from the collimator as a parallel beam. The slit drawtube has a clamp, which may be loosened with a small screwdriver. In handling the tube, be careful not to damage the slit jaws. They are sharp and accurately machined. Never attempt to clean them yourself, consult the instructor if cleaning seems necessary. The slit width is adjusted by rotating the knurled screw. In this instrument the slit is spring loaded so that the jaws cannot be forcibly closed, but on some other instruments one must be very careful when closing the jaws.

7. Leave the telescope arm's clamping screw loosened.

PRE-LECTURE CHECKLIST

1. Point out that the spectrometer is a precision instrument, capable of 1% accuracy in measurement of angles, and better than that in measuring the angles required in this experiment.

2. Show the students how to lift or carry the spectrometer. First tighten the telescope screw finger-tight, then lift the spectrometer by its base only, NEVER by the telescope or collimator arms.

3. Remind students that precision instruments should never be forced in any way. Clamping screws should be turned finger-tight only, never forcibly. Clamping screws facilitate use of the fine adjustment screws. The clamping screw associated with a particular adjustment should always be loosened before making that adjustment, for the screw can score (scratch or gouge) the precisely machined bearing surfaces, making future adjustments difficult.

4. Point out the where the cross hairs are located. Warn against pushing anything down the tube that would break them.

5. Explain and demonstrate the auto-collimation procedure. Emphasize that once the cross hairs are in the correct position, the eyelens may be adjusted to any position that the user finds comfortable, and may be readjusted at any time without affecting the precision of measurements.

6. Demonstrate the prism table leveling procedure. The reason this is tricky is because the prism has several degrees of freedom, and these interact. If you attempt this by trial and error, you soon become frustrated, for one adjustment can disrupt a previous one. The philosophy behind a good procedure is to place the prism on the table in such a way that adjustments can't interact with previous adjustments. This is a nice example of engineering "constraint" problems, which one encounters frequently in science.

7. Warn the students against touching the 5000 volt terminals of the spectrum tube power supply. The current is quite low and unlikely to kill anyone, but the experience is sufficiently unpleasant that I have never seen a student deliberately repeat it.

8. Explain how the control rheostat is connected. The spectrum tubes should be operated only brightly enough to see and measure the desired lines. Operating them at high intensity shortens their life.

9. It is helpful to manually demonstrate the process of finding minimum deviation. Ask students to watch the prism as you rotate it in one direction while you verbally describe what you see: "The spectrum is moving to the right; it's slowing down; now turning around; now moving to the left." This simple demonstration is actually quite effective in getting the idea across. This can be set up with a prism and a beam of light projected through the prism and onto a wall.

10. Set up a spectrometer to show the mercury spectrum. Let each student look at it. Emphasize that if the two yellow lines can't be resolved, then either the slit is too wide, or the instrument is out of focus.

NOTES ON PROCEDURE

Since minimum deviation is so easy to obtain (after it is done once) I now ask students to measure each spectral line at its minimum deviation. Then one can plot a dispersion curve of n vs. λ, rather than merely a deviation curve of δ vs. λ. One has the ability to get minimum deviation for each line in naked-eye spectroscopy. In spectrography, where the spectrum is photographed, you can only set the prism for minimum deviation for one particular line, usually a bright line near the middle of the spectrum.

A Pellin-Broca prism has the desirable feature that when the deviation is 90° the prism is at minimum deviation for whatever wavelength is being observed. This makes it practical to design a spectroscope in which the telescope makes a fixed angle of 90° with the collimator, and the engraved scale measures rotation of the prism. This scale can be calibrated in wavelength, for a given prism.

Many laboratory manuals suggest that students measure the telescope angle when looking straight through at the slit, implying that this reading is to be used as a reference "zero." This is, in fact what students usually will do if not better instructed. Most laboratory manuals do not point out that it's much better to measure each line's deviation both left and right, then take the difference of these and divide by two to obtain the deviation. This procedure immediately doubles the precision of the determination of the minimum deviation. If students have gotten into the habit of looking for ways to improve precision, they will do this without being asked. I never suggest it to students, being interested to see how many care enough about the quality of their results to discover it for themselves. None have, in over 25 years I've observed freshman laboratories. None of the students in advanced optics discover it either! The fault seems to be that students are not concerned with improving the results, are not critically examining experimental and mathematical procedures and are not looking for better procedures. They fall into the habit of being mere "instruction followers." They are simply not "involved" in the experimental process beyond what they feel are the minimum requirements to "get by." The fault, of course, is ours, if we let them get by with this behavior.

In fact, there's no place in this experiment where one would ever have to, or want to, use the "zero" angle position. We have occasionally used lab manuals that explicitly suggest measuring each spectral line's deviation both left and right. What do the students do? They subtract the zero reading from each deviation position, then average the two deviation angles! Apparently our discussion of the data-cancelation in the "method of differences" when we did the free-fall experiment had absolutely no transference!

In the same spirit, I do recommend that the prism angle be measured by recording the angle of beams from both sides, taking the difference, and dividing by two. Some references (Valasek) recommend using the Gauss eyepiece to measure the normal to the two faces, then taking the difference. This difference is about 60 for an "equilateral" prism. The method I suggest gives a measured angle of 120, which is more precise if a sufficiently narrow slit is used. My method could have a determinate error if the collimator's exit rays are not exactly parallel, that is—if the collimator isn't perfectly collimated.

NOTES ON THE ALIGNMENT PROCEDURE, added April 21, 1991.

Over the years we have recommended various methods of spectrometer alignment, and have used manuals that sometimes recommend particular methods. Some manuals are silent on this matter!

* The Gaertner-Peck Spectrometer Manual, supplied with our model of spectrometer, recommends the use of an accessory optical glass adjusting plate, with nearly parallel faces. Using the Gauss eyepiece one looks at the reflection from one face, then rotates the plate 180°. The plate faces are parallel to the spectrometer axis when the return image of the cross hair keeps its same height after a 180° rotation of the plate. A two step process is used. The reflected image from one face is made to coincide with the cross hairs. The glass plate is rotated 180°. The images are brought half way into alignment with the telescope tilt adjustment and the rest of the way with the prism table tilt adjustment. The process is repeated if necessary until rotation of the plate makes no difference. When this is achieved, the telescope tilt is correct with respect to the spectrometer axis. The plate surfaces are parallel to the spectrometer axis also, but this does not ensure that the prism faces will be when placed on the prism table.

* Valasek's book recommends the same method, but with a two-sided mirror, both sides being silvered!

* Wall and Levine's manual (Appendix J) describe an initial approximate alignment using a spirit level! The level is placed successively on the main scale plate, the prism table, and finally the telescope and collimator. They remark that "complete adjustment of the spectrometer is a long and arduous task for the novice." They then describe a "better" procedure, which, as presented, is a long and arduous one. It is deficient in that it does not recommend a position of the prism on the table which will avoid interaction of adjustments. The procedure does not make use of a Gauss eyepiece.

* Skolil and Smith give quite complete alignment instructions (Appendix I-K, p. 173). Their method is based on sound principles, but suffers from having a step in which the student must turn two screws equal and opposite amounts! This is mathematically correct, but not an easy task, for there are no visual clues to guide the experimenter to do this precisely. Their procedure also requires the student to rotate the prism on the table 180° in one of the steps.

* Wagner's book Experimental Optics is one of the few books that clearly sets down the conditions required for precision measurements with the spectrometer:

1. The principal axes of the telescope and collimator must be perpendicular to the main axis of the instrument, i.e., the axis about which the telescope and prism table rotate.

2. The telescope must be focused for parallel incident rays, that is, for infinity.

3. The collimator must be focused for parallel emergent rays.

4. The prism must be adjusted so that the faces which include the angle to be measured are both parallel to the axis about which the telescope and table turn.

5. In certain spectrometers...

a) The axes of telescope and collimator must pass through the main axis of the instrument.

b) It must be possible to make the axes of the telescope and collimator coincident.

Wagner then guides the student through a sound and correct procedure, sensibly avoiding the "equal and opposite" screw turning. He emphasizes the importance of the placement of the prism so that one may adjust one face without disturbing the tilt of a previously adjusted face. The procedure has one flaw: the final adjustments of the prism table are made using reflected light from the collimator and centering the slit image on the cross hairs. Wagner makes no mention of the use of a Gauss eyepiece to improve the precision of these final adjustments.

* C. Harvey Palmer's manual is the only one I have found that mentions the use of the prism itself (rather than the accessory plate or mirror) to achieve the correct tilt of the telescope by observing a reflected image of the slit. It is also the only one which suggests (in a brief footnote) that one might use this same method to align both prism faces, if the prism is placed on the table so its faces are normal to the lines joining the table adjustment screws.

Can one use the best ideas from these sources to devise an optimally short and efficient method? At least there are certain things we'd like to avoid:

* Frequent removal or relocation of the prism on the prism table.

* Simultaneous screw-turning!

* Use of extra accessories, like the glass plate or mirror.

* Estimations, like "bring the cross hairs halfway into alignment using screw..."

The latest (April 21, 1991) version I've come up with requires no removal of the prism, or rotation of the prism table during the entire alignment procedure. It places the prism with the unused face (frosted) near the edge of the prism table and leaves it there.

There's a small price to pay. The telescope axis alignment is carried out with light reflected from the prism faces at an incident angle of about 60°. Palmer recommends 45°, which is better, though one wonders why he didn't suggest a smaller value, consistent with the constraints of the instrument. The best choice of all is 0°, obtainable with the accessory plate.

Is a 60° incident angle good enough for the purpose? At 0° a tilt error of θ in the prism face causes the reflected beam to be high or low by 2θ. At 45° it is off by θ. At 60° it is off by 2θ/3. My experience in making this adjustment is that this is indeed good enough, compared with other error sources. I find the error no larger than the error due to "play" or "wobble" in the spectrometer itself. The real virtue of my method is that it doesn't require resetting the prism table during the adjustments. Play in the prism table can cause enough uncertainty to confuse the adjustment process and waste the experimenter's time trying to make adjustments finer than necessary.

If one wants better, one can swing the telescope all the way, as close as it will go to the collimator, then rotate the prism table to view the reflected slit image from one face. Then do the same on the other side. This adds two rotations of the prism table, then a third one to relocate the prism for measurement of the prism apex angle. That's not really much extra complication.

To summarize: The best strategy for a given instrument depends on whether that instrument has a Gauss eyepiece. If it does not, the collimation must be done by focusing the telescope on a distant object, or looking into an already collimated beam from an auxiliary collimator.

The tools available include:

* The Gauss eyepiece.

* Placement of the prism on the table for non-interacting adjustment. Actually all that is necessary is that the alignment of the second prism face not disturb the tilt of the face previously adjusted.

* The auxiliary parallel plate (or mirror). This takes advantage of the fact that when a mirror tilts through angle θ, the angle of the reflected beam changes by 2θ.

* The method of accomplishing an adjustment halfway with one screw and the rest of the way with another. This works with the 2θ condition of the previous note.

* The method (Palmer) of looking at the reflected image when telescope and collimator are at 90° to each other. At this position any vertical tilt error of amount θ shows up as a vertical misalignment of θ in the reflected beam. This is only true for the 90° observation angle. This avoids any "halfway" adjustments or "turn two screws the same amount in opposite directions."

* The method (Palmer) of using a horizontal slit as a reference during the adjustments.

* The method (Simanek) of using one end of the slit image (rather than its center) as a reference during the adjustments, when the instrument does not allow the slit to be horizontal.

REFERENCES ON THE SPECTROMETER EXPERIMENT

Skolil, Lester L. and Louis E. Smith, Jr. Modern College Physics laboratory Manual, 2nd ed., Wm C. Brown, 1974.

Wall, Clifford N. and Raphael B. Levine. Physics Laboratory Manual, 2nd ed., Prentice-Hall, 1962.

Wagner, Albert F. Experimental Optics. Wiley, 1929.

Valasek, Joseph. Theoretical and Experimental Optics. Wiley, 1949.

Palmer, C. Harvey. Optics Experiments and Demonstrations, The Johns Hopkins Press, 1962.

RESULTS

The (American Optical) prisms we use are flint glass. Minimum deviation for the mercury green line is 51.5°. The prism angle is 60°. The index of refraction of the prism is 1.653.

[The deviation is 57°, giving n = 1.67 for the newer prisms.]

A 1° error in the prism angle and in the deviation angle, this causes an error of 0.045 in the index of refraction. The student may be tempted to express this as a percent (3%) but this is inappropriate for a measure which arbitrarily references to a non-zero value (n of vacuum is 1).

If the student doesn't appreciate this point, suggest another example that is more familiar: temperature. Does it really make sense to express error in Celsius temperature as a percent? A one degree error would then be 1% of a 100° temperature, and 100% of a 1° temperature! What if the temperatures were converted to Fahrenheit? In some cases a percent error is meaningful for temperatures measured on the Kelvin scale, but even in that case one must consider the matter very carefully.

It is not practical to derive a standard form error equation for this experiment without calculus. Non-calculus students would be better advised to insert the errors into the equation for index of refraction and recalculate the whole equation.

A common mistake in the calculus method of calculating the error is to forget that the deviation angle, d, is in radians.

ANSWERS TO QUESTIONS

Violet (left).......Red (right)

(1) If you were a perceptive observer, you noticed that the spectral lines were curved. This is illustrated (exaggerated) in the figure. If you have scientific curiosity, you may have wondered why they were curved. You can figure this out by considering the geometry of rays passing through the spectrometer, originating from various points on the slit, say from top, bottom, or middle of the slit. (a) Explain why the lines are curved. (b) Show how you can tell which way they should curve (i.e., in the diagram: is side A the red end of the spectrum, or is it side B?). (c) What shape is the curve that geometric theory would predict? Is it a circle, ellipse, parabola, or something else? You can't tall this just by the visual appearance of the lines.

Rays from the top and bottom of the slit emerge from the collimator at an angle to the collimator axis. They have a larger incident angle on the first surface of the prism than do rays from the center of the slit. [This statement needs to be supported with a three dimensional diagram.] Suppose that the prism is at minimum deviation for rays coming from the center of the slit. Rays from the slit ends will have a greater incident angle at the prism face and therefore a greater final deviation than those from the slit center. The violet end of the spectrum is the end which is deviated most by a prism. Hence the ends of the lines will appear bent toward the violet end of the spectrum.

Observant students will notice that if the prism is set well off of minimum deviation, the curvature of the lines appears somewhat greater. This is what one would expect from the above explanation, for the deviation curve has the smallest slope near minimum deviation, and much greater slope away from minimum deviation. This is also the definitive experimental test that our explanation of slit curvature suggests. Observant students will also notice that the dispersion of the spectrum is greater if the prism is not at minimum deviation.

The curvature of the spectral lines is very nearly parabolic. I don't expect freshman to be able to derive this fact, but they might discover it from library research. For example, in the excellent book Theoretical and Experimental Optics by Joseph Valasek (Wiley, 1949), p. 95, we read:

Spectrum lines are naturally curved because of the greater deviation of skew rays than those travelling in a plane at right angles to the refracting edge. The curvature is approximately parabolic, the radius at the vertex being:

R ≈ n2 f [tan(i)]/(2n2 - 1)

where f is the focal length of the lens and i is the angle of incidence. The curvature changes very slowly with wave length, so that it may be compensated by using a curved slit. This compensation at either the exit slit or the entrance slit, is important in a monochromator, or a spectroscope using a photocell or thermopile at the receiving end.

One would predict, therefore, that the spectral lines from a diffraction grating would not be curved. They aren't. (1) Students ought to notice this fact and comment on it.

I have had to read through an awful lot of student "answers" which consisted of some true statements which had nothing to do with the question. I've also seen many statements and assertions strung together which had no logical connection with each other.

"The rays from the top and bottom of the slit travel farther." True, but this has nothing to do with the question or its answer.

"The lines are curved because the lenses have curved surfaces." No comment needed!

"It is caused by spherical aberration." Innovative!

"The faces of the prism aren't quite flat."

(2*) The determinate error equation for Eq. 1 is:

Δn = ΔD {cos[(A+D)/2]/(2sin[A/2}} + ΔA (n/2){cot[(A+D)/2] - cot[A/2]}

Derive this result. See next page.

(3) What absolute error in the index of refraction results from an error of one minute of arc in the deviation angle? Assume glass of index 1.7 and a wavelength of 5461 Ångstroms.

A 1' error in deviation angle will cause an error of 0.00167 in the calculated value of n. Round to 0.002.

(4) Under the same assumptions as question (2), what absolute error results from a one minute of arc error in the prism angle?

A 1' error in prism angle determination causes a 0.0025 error in the calculated value of n. Round to 0.002.

[The error analysis to justify these results will be found below.]

(5) What are the special advantages of using minimum deviation, rather than using a larger deviation where the spectral lines are spread apart more?

The minimum deviation method makes it unnecessary to know or measure the angle of the rays incident on the first face of the prism. That is, you don't need to measure the prism's position relative to the spectrometer. If the prism were not at the position for minimum deviation, the prism's position would need to be known. That would introduce another source of experimental error, and you'd have a terribly complicated equation for n. Also, at minimum deviation, an error in the prism table position makes a very much smaller error in the results, and is negligible.

I am told that Newton is responsible for the method of minimum deviation. It does not appear in his published papers or books, but in a letter to someone who was repeating Newton's experiments.

Some consequences of the minimum deviation situation are interesting, but not particularly noteworthy as useful advantages:

* The rays pass symmetrically through the prism, and within the prism are perpendicular to the bisector of the refracting angle.

* The spectrometer has maximum aperture. This is only important if the prism is undersized.

* The image of the slit has minimum astigmatism.

DERIVATION OF THE ERROR EQUATION:

First, consider the case where the error is predominantly in the deviation angle D, the error in the prism angle A being negligible.

n + Δn = sin [(A+D+ΔD)/2]/[sin [A/2] .

where ΔD is a determinate error in D. Separate the (A+D)/2 from the ΔD/2 and then use the well known trig identity on the numerator.

sin[(A+D+ΔD)/2] = sin[(A+D)/2] cos [D/2] + cos[(A+D)/2]sin[ΔD/2]
= sin[(A+D)/2] + (ΔD/2)cos[(A+D)/2]

so

n + Δn = {sin[(A+D)/2] + (ΔD/2)cos[(A+D)/2]}/sin[A/2]

n + Δn = sin[(A+D)/2]/sin[A/2] + [ΔD/2]{cos[(A+D)/2]/sin[A/2]}

so therefore:

Δn = [ΔD/2]{cos[A+D]/2}/[sin[(A+D)/2]

A = 60° and D = 57° for n = 1.65 flint glass. For these values, this would be (ΔD/2)(0.5225/0.5) = 0.522 (ΔD). If the error in D is about 0.1° = 0.02 radian, then the error in n is 0.01.

Now consider the case of an error in the prism angle, A.

sin[(A+D+ΔA)/2] = sin[(A+D)/2] cos [ΔA/2] + cos[(A+D)/2] sin[ΔA/2]
= sin[(A+D)/2] + (A/2) cos [(A+D)/2]

n+Δn = {sin[(A+D)/2] + (ΔA/2)cos[(A+D)/2]}/{sin[A/2] + ΔA/{2cos[A/2]}

This looks like a mess at first, but notice that it is in the form where the "error in the numerator" and the "error in the denominator" explicitly show, so since the fractional error in the quotient is the fractional error in the numerator minus the fractional error in the denominator

Δn/n = [ΔA/2]{cos[(A+D)/2]/sin[(A+D)/2] - [ΔA/2][cos[A/2]/sin[A/2]

However, the fractional error in n is not a meaningful way to express the error in n so this should be converted to the absolute error in n:

Δn = n(ΔA/2){cot[(A+D)/2] - cot[A/2]}

This goes a lot easier with calculus!

Since both A and D are about 60°, this can be done in one's head:

Δn = (ΔA/2) 1.65 (89.02 - 88.09) = (ΔA/2) 1.65 (0.93) = 0.767 ΔA.

Now if ΔA is, say 0.1, that's about 0.02 radian, for an error of 0.015 in n. [Actually, the error in A will be less than this.]

One could now put the two error equations together into one grand-slam complete error equation!

Δn = ΔD [cos[(A+D)/2]/[2(sin[A/2]} + ΔA (n/2)[{cot[(A+D)/2] - cot[A/2]}

If the student consistently measured angles both left and right, taking their difference and dividing by two, the error in n should be about half of the estimates above, because the error in A and D would be half as much as if they were obtained from measurements on only one side of "zero."

L-4 SPECTROMETER, Grading checklist, when the grating experiment was combined with the prism experiment:

Question 1: Why are the spectral lines curved?

Question 2: Error due to 1 error in deviation angle?

Δn = 0.00016, for = 51.5° and A = 60°

Question 3: Error due to 1° error in prism angle?

Δn = 0.0004, for = 51.5° and A = 60°

4 and 5. Values for D and n.

Two kinds of prisms: D = 51.5°, n = 1.653 (Freshman lab)

D = 57°, n = 1.67 (0.995 radian)

Both are flint glass.

6. The uncertainty in n is 0.02 if scale reading errors are assumed to be 0.5°. [A very conservative estimate.] If errors are smaller, one can assume linearity of the error propagation.

The statement of error must include a statement of the assumed data error and justification of how it was determined. It also must include the method used to calculate the error propagation.

7. Derivation of formula for part (4). [A = a/2.]

8. Graph of deviation angle vs. wavelength.

9. Did the student measure the refracting angle A, rather than just assuming it?

10. Did the student measure lines from a second spectral source? Is there a clear statement of how well the experimental values agree with handbook values?

11. Grating data compared with the prism data.

12. Value of grating constant. 2.54 x 10-4 cm.

CHECKING RESULTS

Here's a BASIC program to quickly check the results:

10 'SPECTROM.BAS, by Donald Simanek.  Calculates n for prism.
40 PI = 3.1415927
45 SCREEN 2:CLS:LOCATE 1,1,1:'visible cursor
50 PRINT "INDEX OF REFRACTION OF A PRISM, by Donald Simanek
51 PRINT
52 PRINT "    sin [(A+D)/2]"
53 PRINT "n = "
54 PRINT "      sin [A/2]"
55 PRINT
60 PRINT "Enter degrees and minutes separately, as prompted.
70 PRINT "If you enter degrees in decimal form, just hit 'enter' at minutes prompt.
80 PRINT:PRINT "Prism angle, A: degrees [default: 60]";
90 INPUT
95 IF A=0 THEN A=60 :'Sets default, and traps for division by zero.
100 PRINT "Minutes";
110 INPUT AM
120 A = A + AM/60
130 IF A=0 THEN A=60
140 PRINT:PRINT "Minimum deviation angle, D: degrees";
150 INPUT D
160 PRINT "Minutes";
170 INPUT DM
180 D = D + DM/60
190 N = SIN(PI*(A+D)/360)/SIN(PI*A/360)
200 PRINT:PRINT "A = ";A;", D = ";D
210 PRINT "The index of refraction, n = ";N
220 PRINT:INPUT "Another calculation [Y/n]";R$
230 IF R$="N" OR R$="n" THEN 300 ELSE 45
300 SYSTEM

Text and line drawings © by Donald E. Simanek, 1994, 2004.


Comments on spectrometer experiment reports.

Results should appear in the results section. Don't make the reader look elsewhere.

You need to indicate how you obtained your error estimates in data, and what contributing factors caused them. Some said the error in angles was 1° arc. That's about the error in reading the scale. But did you also consider the larger error in locating the cross hairs on the spectral line? If so, no one said so! The spectral lines have width, and may show parallax with respect to the cross hairs if the telescope collimation wasn't perfect. This is the dominant error source, not the scale reading error.

Hardly anyone indicated how they got from the data error to the error in the result. If you plugged in values of angle and calculated the result (n) three times, say so.

In many cases, where results were shown for several spectral lines, the errors were obviously larger than your stated error, which should make you suspicious.

Many people didn't say whether they measured the prism angle, or just assumed it was 60°, nor did they say how they measured it, and whether they measured it by more than one independent method.

Some students showed a graph of index of refraction vs. wavelength. That's good. But is not supposed to be a straight line. These graphs clearly showed that your experimental errors were larger than you claimed, for the curve should be gently curved and very smooth.

A common blunder was to use telescope position readings in place of deviation values. This suggests that some students didn't understand the equation, or how the spectrometer worked.

Some people gave a `refractive index for the prism' but didn't indicate what color light it was for. The prisms you used this year were flint glass, with refractive index of about 1.65 for the 5461Å green line of the Mercury spectrum.

The deviation angles aren't worthy of listing as results. But they should be somewhere in the report, at least in the original data sheets. We want to see index of refraction results. In some cases the indices were too high or too low, yet I found no original data sheets, or values of deviation to allow me to check where the blunder occurred.

Reread the chapter 9 on lab report writing in the red book. Personal comments about how much you learned or how much you liked the experiment are not appropriate in a report. See also the document on technical report writing from Rensalaer University linked on my home page. I also have similar documents from Penn State, if you'd like to consult them.

The prism equation for minimum deviation is not called Snell's Law. It is derived from Snell's Law.

Willebrord van Roijen Snell (1591-1656) was a Dutch mathematician. Though Ptolemy knew about refraction, his law of refraction was only valid for small angles to the normal. Snell's discovery of the correct refraction law did not become well known, and when Descartes published it later he didn't credit the source. Johannes Kepler seems to have independently discovered it as well.

Several people had identical or nearly identical reports. Since I cannot determine which of these was the author, or whether it was a group effort, I divided the score by 2. Partners work together in lab and will therefore have identical data. Partners may study together, but when it comes to writing the report, do it alone, in your own style and your own words. You should do your own calculations, and draw your own conclusions as well, not influenced by anyone else.

Endnotes:

February 28, 1996

1. Spectral lines formed by a diffraction grating are curved when seen in the grating spectrometer, but a lot less than in the prism spectrometer. This is due to refraction through the thickness of the protective glass plates the replica grating is mounted between, but not caused by the grating itself.