UNIVERSITY OF CAPE TOWNPHYSICS PHYLAB3 LABORATORY

OPTICAL SPECTROSCOPY

The aim of this experiment is to determine some of the characteristics of an optical spec-trometer, and investigate some emission spectroscopy. Before starting the experimentyou should read the Physics PHY322S Laboratory Notes on Optical Spectrometers. Thespectrometer is a Heath EU-700 Czerny-Turner scanning monochromator with a photo-multiplier detector and pulse-counting electronics. You will investigate:

1. the linearity of the system — is the output count rate proportional to the intensityof the input light?

2. the spectral response function — how does the output count rate depend on thewavelength of the input light?

3. the instrumental line shape function and the resolving power — what line shapedoes the spectrometer give for a monochromatic input; how far apart must twospectral lines be so that they are recorded as two distinct lines rather than as asingle broad line?

ApparatusThe block diagram shows the experimental equipment.

The computer is used to control the monochromator scanning and to acquire spectra.There are some notes on this in the laboratory but you may need some extra help; askthe lecturer in charge if you have problems. Two light sources will be used, a HeNe laser

(λ = 6328Å) and a tungsten filament lamp. Since both of these take about half an hour toreach their final operating temperature they should be switched on well before recordingspectra.

Initial alignment

Investigation of the linearity of the system and of the spectral response function will bedone with the tungsten filament lamp as the light source. The input optics should beconfigured as shown below. The lenses should be inserted one by one (from left to righton the diagram) ensuring that the light is centred on the slit after each insertion.

Linearity

If a beam of unpolarised light of intensity I0 is incident on two LPs in series, the emergentintensity I(Θ) is given by Malus’ law:

I(Θ) =1

2I0 cos

2(Θ)

where Θ is the angle between the transmission axes of the two LPs.

Set the monochromator at a wavelength between 4000 and 5000Å, and adjust the slitwidth to get a count rate on the order of 104 per second with the transmission axes ofthe linear polarisers aligned (Θ = 0). Record the count rate as a function of the angle αdisplayed on one of the LP scales. Note that you will have to figure out how Θ is relatedto α. Plot an appropriate graph to investigate the linearity of the counting system.

Spectral response function

If C(λ) is the output count rate and L(λ) is the input light intensity, the spectral responsefunction S(λ) is defined by C(λ) = L(λ)×S(λ). (The units here are not usually significantsince one is almost always interested only in the relative rather than the absolute values.)

Thus to determine the spectral response function of an instrument one needs a sourcewith a known intensity distribution. A hot tungsten filament is a good approximation toa black body, for which the intensity distribution is the well-known Planck distribution.You will acquire spectra of the light from a tungsten lamp, calculate the appropriateblack body function, and take the ratio of these at a set of wavelengths to get the spectralresponse function.

To give an overall picture of the instrument response a spectrum should be measured overa wide wavelength range . Use manual scans to determine what range the computer scanshould cover. Since high resolving power is not required here the slit width is not critical– try 100 µm. The main features of this spectral response function should be discussedwith reference to NOS Fig. 13 (NOS = Notes on Optical Spectroscopy). You should alsodiscuss the possibility of whether the second order spectrum could affect your results.Since nλ = 2d cos φ sin θ, radiation of wavelength 200 nm in second order will appear atthe same angle θ as radiation of wavelength 400 nm in first order, for instance.

A second spectrum should cover the range 3600 to 3700Å. This will be used in the laterexperiment Optical Spectroscopy 2 to determine the actual intensities of spectral linesfrom mercury discharges.

Black body radiation

The intensity I(ν) of the radiation emitted by a black body is given by (c/4)u(ν), whereu(ν) is the energy density of radiation in a cavity at a temperature T , given by the Planckradiation function, which can be expressed either in terms of frequency ν or of wavelengthλ:

u(ν)dν =8πhν3

c31

ehν/kT − 1dν

u(λ)dλ =8πhc

λ51

ehc/λkT − 1dλ

where h is Planck’s constant, 6.63× 10−34 J sc is the speed of light, 3.00× 108 m s−1k is Boltzmann’s constant, 1.38× 10−23 J K−1.

The decision about which of the two forms above is appropriate for use in this experimentrequires some thought. Notice that in both equations a dν or dλ appears, but the functionone actually calculates does not include these differential elements. The slit width ∆xremains constant as you acquire a spectrum, but what happens to ∆ν and ∆λ? Look atthe expression for the reciprocal linear dipersion of the monochromator (NOS Eq. 12) anddecide which of ∆ν and ∆λ has the smaller relative variation over your chosen spectralrange.

Another point to think about is that this experiment is a photon counting experiment:the numbers sent to the file correspond to the numbers of photons detected at particularwavelengths. Is this going to affect the form of the theoretical function that you use?

Radiation from tungsten lamps

Before one can calculate the input intensity function, one must know the temperatureof the tungsten filament. This is determined from the resistance of the filament whenhot (which you will measure) and when at room temperature (which is given). Data fortungsten, taken from the CRC Handbook of Chemistry and Physics, are presented on afollowing page. The dependence of resistivity on temperature can be approximated by

ρ(T ) = ρ(TR)[1 + b∆T + 0.02b2(∆T )2]

where TR is the room temperature, ∆T = (T − TR), and b = 4.5 × 10−3 K−1. Will thedependence of resistance on temperature be identical to that of resistivity on temperature?

To obtain the input intensity as accurately as possible one should take account of the factthat a tungsten filament is not a perfect black body. The emissivity e of tungsten is notindependent of wavelength, in contrast to the case of a perfect black body for which theemissivity is by definition unity for all wavelengths, so Itungsten(λ) = e(λ)Iblackbody(λ). Dataon the emissivity of tungsten appears later in these notes. A straight line fit “by eye” to thedata for T = 2400 K over the wavelength range 350 to 700 nm gives e = 0.527−1.53×10−4λwith λ in nanometres.

Instrumental linewidth and resolving power

A naive geometrical optics approach predicts that for monochromatic light the instru-mental linewidth will be proportional to the slit width. If this were true one could obtainarbitrarily small linewidths by reducing the slit width. In reality there is a lower limit tothe attainable output linewidth, or equivalently, an upper limit to the resolving power. Toinvestigate the resolving power of a spectrometer one needs a monochromatic source. TheHeNe laser is a convenient source of essentially monochromatic radiation (λ = 6328Å).

Without any lenses in the beam path, make sure that the HeNe beam is centred on themonochromator slit. Insert a short focal length converging lens, as below, and again makesure that the expanded beam is centred on the slit; this should give an essentially uniformintensity over the slit. The two linear polarisers (LPs) are used to control the intensity ofthe light incident on the slit.

Acquire spectra in the region of 6328Å for slit widths up to at least 100 µm. You willneed to use the LPs to adjust the intensity of the light in order to get suitable count ratesfor the different slit widths. If your graphs do not have the expected shape this may be anindication that the input optics are not correctly aligned. Make linewidth measurements(FWHM) and plot a graph of linewidth against slit width.

From NOS Eq. 9 find the angle φ of the grating for the HeNe wavelength, and hence find(NOS Eq. 12) the reciprocal linear dispersion at this wavelength. On the same axes asyour experimental results, draw a graph (like NOS Fig. 8) for the “geometrical opticslinewidth” vs. slitwidth.

From your experimental results, determine the maximum resolving power of the monochro-mator and compare this with the value predicted by NOS Eq. 6. Although the gratingin the Heath monochromator has a width of 40 mm, it has been masked off so that onlythe central 9 mm are used. This has been done to minimise optical aberrations (sphericalaberration, coma, etc.).

One way to check the effective grating width is to investigate the spacing of the subsidiarydiffraction maxima observed with a small slit width. To observe these subsidiary maximait may help to increase the intensity, giving an “overexposed” central maximum. Recorda spectrum in this way and hence get an estimate of the grating width.

Some final points

1. The light from the HeNe laser at λ = 632.8 nm was referred to as “essentiallymonochromatic”. In fact typical low power laboratory HeNe lasers operate on sev-eral longitudinal modes simultaneously, each longitudinal mode being a standingwave in the laser cavity. The condition for a standing wave in a laser cavity oflength L is qλ/2 = L where q is the longitudinal mode number, an integer. Thusthe linewidth of the incident radiation can be taken as several (say three) times thespacing of the longitudinal modes.

For L = 30 cm find the frequency spacing δν between neighbouring modes, andtake the frequency spread to be ∆ν ' 3δν. Hence show that the wavelength spread∆λ ' 2 × 10−3 nm and compare this with the minimum linewidth measured. Is itjustified to neglect the departure from monochromaticity of the laser light?

2. What do you think are the meanings of the terms brightness temperature and colortemperature in the CRC data sheets?

Emission spectroscopy

Set up the input optics as shown below so that the light from either the low pressuremercury source (a Geissler tube) or the high pressure mercury source (a commercialmercury discharge lamp, similar to the ones used for street lighting) can be directed tothe monochromator entrance slit. The high pressure lamp should be switched on at leasthalf an hour before acquiring spectra to allow it to reach its equilibrium temperature(and pressure). When using the high pressure lamp you will probably need to reduce theintensity at the spectrometer entrance slit by using the two linear polarisers. The Geisslertube is much less intense, and the LPs may not be required.

(a) Line shapesLine shapes can often be used to obtain information about the environment of the emittingatoms or molecules. In plasmas, for instance, the line shape will depend on the chargedparticle concentration and on the temperature. Since the measured line shape will be aconvolution of the intrinsic atomic line shape and the instrumental line function, accuraterecovery of the intrinsic line shape is not in general a simple procedure. However onecan often obtain rudimentary information about the intrinsic line width (the FWHM, forexample) by elementary methods. In the special case when the instrumental width issmall compared to the width of the line under study – the spectroscopist’s dream – theobserved line shape will be a good approximation to the intrinsic atomic line shape.You are required to determine the shape of the 4358Å line for both the mercury sources,as accurately as possible with the Heath monochromator. On the basis of your experiencewith the experiment Optical Spectroscopy 1, choose an appropriate slit width and acquirespectra of the line. From the observed linewidths obtain estimates of the intrinsic atomicline widths. Compare the line widths for the two sources, and comment on the line shapes.Spectral lines are broadened by a number of physical processes. You need not go into thedetailed theory of these effects, but you should read through the appropriate portions ofa book on spectroscopy to get a feeling for the basic ideas.

(b) Line intensitiesThe relative intensities of lines from a particular source can also give information aboutthe atomic environment; the temperature of the source is the most obvious factor thatwill influence relative intensities since the populations of the various states will depend onBoltzmann factors, exp(- ε/kT ). However in many cases the source may not be in thermalequilibrium, and other factors may influence the relative populations of the excited states.

There are three mercury lines between 3645 and 3665Å; acquire a spectrum over this rangefor both the mercury sources. One should always bear in mind that the observed intensitiesmay not correspond to the values as emitted by the source, since the spectral responsefunction of the instrument in use may not be “flat”, i.e. independent of wavelength. Usethe spectral response function of the monochromator/photomultiplier as determined inthe Optical Spectroscopy 1 experiment to correct the observed intensities.

Consider the relative intensities of the three lines in the two cases, and compare your valuesfor the relative intensities with those given in the NBS tables (see following pages). Readthe Physics 300 Laboratory Notes on Spectral Line Intensities and Optical Thickness, anddiscuss.

Bibliography

There are many books on the theory and practice of optical spectroscopy; the two listedbelow give good general introductions to the basic ideas.A.P. Thorne Spectrophysics Chapman and Hall (1988)J.M. Hollas Modern Spectroscopy Wiley (1987)

(Based on an experiment devised by Prof HST Driver, Physics, UCT)

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