Liliana Bruzzone
and Martin E. Roselli Universidad Nacional d e La Plata La Plots, Argentina
I
I
Wavelength and Spatial Distribution of the Light from- a Monothromator
While the slit-width effect on the shape and spectral distribution of the light band issuing from the exit slit of a monochromator is a subject which is treated virtually in every textbook on instrumental aualysis (1-31, discussions are usually restricted to qualitative descriptions of the triangular shape and definitions of spectral-width and effective hand-width. Such a qualitative description leaves the student with a poor idea of hand-width. Other hooks (4-6) give a more extensive discussion and the one by Parker (71, specializing in photoluminescence, gives sufficiently detailed instructions for determining a monochromator's band-width. In this work we introduce a simplified procedure of measurement and calculation for students without a solid background in optics. Although the approach is by no means rigorous, it is suitable for class-room demonstrations a t the introductory level.
LISI
Sz
Figure 1. Optical equivalent design of a monochromator.
Figure 2. Top view diagram of the monochromator section of the Spectranic 20. (1) entrance slit. (2) exit slit and shutter, (3)grating, (4) wavelength scale, (5) sample holder.
General Considerations
The instrument used is the Bausch & Lomb Spectronic 20, single-beam spectrophotometer.l The operation of the instrument and the optical diagram are given in its operating manual. The monochromator system consists of a diffraction grating, lenses, and a pair of fixed slits. The grating disperses incident light independently of wavelength; bandwidth is constant because of fixed slits. A simplified schematic equivalent to its optical principle, is shown in Figure 1. The light passes the field lens, LI, entrance slit, S I , and is focussed on the objective lens, 4.This lens magnifies and foccusses the image of the entrance slit a t the exit slit, Sz, after it has been dispersed and reflected by the diffraction grating. When working with a discontinuous source of light, the images may he regarded as the linear geometrical images of the entrance slit a t the focal plane. If the radiation is continuous rather than truly monochromatic, as is generally the case with most monochromators, the image will be an infinite array of overlapping wavelengths. In both cases the degree of overlapping depends on the width of the entrance slit and the optical characteristics of the monochromator. Thus keeping constant all other optical characteristics, the extent of overlap a t the focal plane can be varied by narrowing or widening the entrance slit. At the focal plane, the length AX in the spectrum corresponding to a wavelength range AX in the image, defines the relation AX/AX called the linear dispersion, m, expressed in millimeters per nanometer, mm/nm; thus the wavelength range of the image, corresponding to a distance AX, will he AX = AX/rn. The exit slit, Sz, located a t a convenient point in the focal plane, selects a narrow band of wavelengths to reach the detector. The intensity versus wavelengths for this radiation represents the wavelength distribution of the light issuing from the monochromator. Intensity and purity of this spectral distribution depend upon both slits; the exit slit collects the light that passes through the entrance slit and the amount of light is proportional to the width of both slits. If the entrance and exit slits are equally wide, the wavelength distrihution exhibits a triangular shape, while when the entrance slit is narrower or wider the shape is
Figure 3. A , exit slit: 8 , shutter;A', modified width of the exit siit.
trapezoidal; only when the size of one slit is much smaller than the other, will the distrihution he rectangular. Entrance and exit slits of different width; can be interchanged without altering the wavelengths distrihution, but the spatial distrihution of light will he concentrated on a different area of the exit slit. The Experiment
The cover is taken off, following the instructions in the instrument manual: the bottom door is removed, together with the tungsten lamp. A black cardboard (cut to match the phototube opening) is put in place and fastened with black plastic tape. The instrument is mounted on two lateral supports so as to assure a separatmn of around 20 cm from the top of the bench. Figure 2 shows a top view diagram of the monochromator section of the instrument eivine the ~ositionof the shutter and exit slit. The two screws whych hold fak both the shutter and the exlt slit are removed, the shutter, B, Figure 3, withdrawn and the slit, A, replaced, Figure 3. A mercury Pen-Ray2 or similar lamp is placed at the opening of the light source and is turned on. The wavelength scale is set at 546 nm and the exit slit is covered with a white cardboard. The light control is fully opened and the mercury lamp displaced until the mercury green line is focussed on the slit. If this cannot be done, the instrument must be calibrated according to the instructions in the operating manual. The lamp is turned off and both the cover and cell-holderreplaced. The instrument and mercury lamp are turned on, and reading checked not ta he greater than 100% T at 546 nm. The dial is set at 525 nm and a scan is made up to 510 nm registering readings 'The Bausch & Lomb, Spectronic 20 Calorimeter-Spectrophotometer, Catalog 33-29-59, Bausch & Lomb, Rochester, New Yark. Ultra Violet Products. Inc., San Gabriel, California. Volume 50, Number 10, October 1973
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each 2.5 nm. Relative transmission values-maximum heing set at 100-are plotted against wavelength. Under these experimental conditions slit widths do not permit the complete resolution of the 577 nm line and values above 560 nm should be dropped. A change in the distribution of wavelengths requires the modification of one of the slits' widths. Any alteration of the entrance slit necessitates removing the focussing system of the Spectronic 20, and this means a further adjustment and calibration of wavelength. As the same effect is attained by modifying the exit slit, and in this instrument it is much simpler, this is the logical alternative. The exit slit is withdrawn and a black plastic tape is attached an both sides along the borders and parallel to the slit, A', leaving an opening of approximately 1 mm wide, Figure 3. The slit is assembled in its original position and the instrument is arranged as before. In this case, as the mercury 546 nm line is not intense enough it is advisable to use the 436 nm line. The wavelength dial is set at 425 nm and a scan run up to 450 nm, registering readings each 2.5 nm. Intensity is again plotted versus wavelength, assigning a value of 100 to the maximum transmission. Discussion
The Bausch & Lamb "Spectronic 20" spectrophotometer is equipped with two unequal slits; the entrance slit is 1.5 mm wide and the exit one, 2.5 mm. The width of the slit image on the plane containing the exit slit is around 1.7 times the aeometrical width of the entrance slit, and this image ma.$ be considered as the geometric image of the slit after being augmented by the optical system of the instrument, itfunciioning, thus, a s if hoth slits were equally wide. The distribution for equal slits may consequently be calculated by taking the following values: set a t A = 546 nm, image width of the entrance slit S1, AX = 1.5 X 1.7 = 2.5 mm; width of the exit slit Sz = 2.5 mm; linear dispersion, m = 0.125 mm/nm. Interval of wavelength given by the entrance slit a t the exit slit plane, AX1 = AXlm = 2.5/0.125 = 20 nm. Wavelength extreme values a t both ends of the interval, A AA1/2 zt 546 10 nm, 536 nm and 556 nm. Now, if we consider the A = 546 nm centered on the exit slit Sz, we have: wavelength range, AAz = Sz/m = 2.5/0.125 = 20 nm, values a t the interval extremes, A + Ah212 = 546 + 10 nm, 536 nm and 556 nm. This means that light reaching the exit slit covers this wavelength range; for this to he possible, the entrance slit must necessarily produce images for every wavelength within this range. Taking the.extreme values as limits, we have: 536 AA1/2 = 536 f 10 nm, 526 nm to 546 nm and 556 + AA1/2 = 556 + 10 nm, 546 nm to 566 nm. In Figure 4B the images of the entrance slit that fall on the exit slit are outlined: thev represent the light concentration on the area of this slit f i r a continuous radiation centered a t 546 nm. Half these imaaes plus other ones exceeding this wavelength range pas; thiough the exit slit. Figure 4A represents the scanning of the mercury 546 nm line, equally wide to the image of the entrance slit a t the exit slit. Vertical dotted lines correspond to the signal detected a t the exit of the monochromator. In position No 5, the image of the entrance slit completely fills the exit slit, thus attaining maximum intensity; this-happens when the monochromator matches the line wavelenath. On hoth sides of this position intensity decreases down to a zero value for a spectral displacement as large as the spectral width of the slit. The spectral width of the hand is given by
*
*
*
2AA = Ahl
+ Ah* = 40 nm
The central wavelength, 546 nm, passes with maximum intensity and the resulting distribution is triangular. At the extremes of the wavelength range given by A -+ AX/2, the intensity is reduced to half of the maximum value; this range is generally named effective hand width. 702
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Figure 4. Wavelength distribution tar A, slits of the same width; C. exit slit narrower: and E. wider than the entrance siit, as the result of scanning of the entrance slit image on the exit siit. 6 ,D, and F. schematic representation of the light concentration on the area of exit slit tor A. C. and E, respectively.
Unequal Slits
The width of the entrance slit of the instrument is left unaltered a t its original value, and the exit slit is narrowed. The same procedure as explained above is applied in the followina calculation for the case of interchanged slits. values between parenthesis corresponding to wjder exit slit: wavelength centered a t A = 436 urn: width of the entrance slit, s;, image AX = 2.5 mm (1 mm); width of the exit slit, Sz = 1mm (2.5 mm). Wavelength range produced by the entrance slit, AX1 = 2.510.125 = 20 nm (1.0/0.125 = 8 nm), A f AA1/2 = 436 10 nm (436 f 4 nm), 426446 nm (432-440 nm). Wavelength range produced by the exit slit, Ahz = 1.0/0.125 = 8 nm (2.510.125 = 20 urn), X + AX212 = 436 + 4 nm (436 f 10 nm), 432-440 nm (426-446 nm). Images produced by the extreme wave10 nm (426 lengths of this range, 432 + Ah112 = 432 AX112 = 426 f 4 nm), 422-442 nm (422-430 nm). 440 + AX112 = 440 10 nm (446 f Ah1/2 = 446 4 nm), 430450 nm (442-450 nm). Distribution of wavelength for the experiment is represented in Figure 4C and in Figure 4 E for interchanged slits; it is seen that the wavelength range given by AX1 AX2 and AAz - AX1 are equal to 20 - 8 = 12 nm. I n each case these ranges pass the exit slit with maximum intensity. Intensity remains constant for scanning positions numbered 3, 4, 5, 6, in the first case and 3, 4, 5, 6, 7, in the second one. On both sides of these positions intensity decreases down to zero when the spectral shift of the image equals the spectral width of the narrower slit. Distrihution, then, assumes the trapezoidal shape indicated. Figure 4, D and F show schemes of light concentration a t the exit slit; in the first case it is concentrated a t
*
*
*
*
*,
Student Results Wavelength Distribution for Equal Slits Width: 2.5 mm: Mercury Line: 546 nm
nrn
0
5 2 0 ; 530 -:
540 550 2AAz40-i
560: nrn
Figure 5 . Experimental data obtained with slits o f equal width
0 0 4 10 15 21.5 26.5 35 40.5 44 46 40 32 26 18 12 7.5
0 0 4.2 8 13 22 28.5 36 41 45.5 45 39 32.5 26.5 19 12.5 7
3
Ah: 20 nm, 2 Ah: 40 n m Linear Dispersion: A X / I A = 2.5120 = 0.125rnrn/nrn
Conclusions
Theoretical calculations represent the ideal wavelength distribution for sources emittine the same number of einsteins per second and wavelength range all through the spectrum. As this is not exactly the case, and because of additional optical imperfections and diffraction phenomena, experimental values differ somewhat from the linearity indicated. In the first case, when using the 546 nm line, the student can realize that the resolution of the 577 nm line is not complete a t the linear dispersion of the instrument because of the separation between the centers of the entrance slit images for both lines as compared with the width of the exit slit. When using the 436 nm line with one of the narrower slits, resolution improves and the 405 nm line does not disturb, in spite of wavelength differences being the same. This illustrates to the student the imoortance of ~ ,~ slit size in defining effective resolving power. The exoeriment imolicitlv involves. besides. the determination of the linear dispersion. In the case of equal slits, the slit width, expressed in millimeters, divided by the effective hand width gives the linear dispersion of the monochromator. ~
Intensity (% T) 2
577 nrn line
the center of the slit, and in the second one, on the extreme borders.
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1
~~
As the mercury line is definitely narrow its intensity varies rapidly with wavelength, so that slight shifts in wavelength setting would result in the determination of correlatively spread transmission values. Nevertheless, the experiment allows reasonably satisfactory results in the hands of careful students. Experimental data typical of students' performance are given in the table. These figures confirm the triangular wavelength distribution and effective hand width indicated in Figure 5. The band-width value resulting from a class average falls within 19-21 nm, in very good agreement with the manufacturers' information. Literature Cited ( I ) Mellon. M. G., "Analytical Ahmmtion
New Ynrk. 195O.o. 201.
-
-
spectroscopy." John
Wiky &
sons, I"
