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    Instytut Fizyki DowiadczalnejWydzia Matematyki, Fizyki i Informatyki

    UNIWERSYTET GDASKI

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    Experiment30: Normal and anomalous Zeeman effect

    I.Background theory.1. Energy levels of electrons in atoms.2. Quantum numbers of electron energy levels.3. Magnetic moment of the electron shell of an atom:

    a) orbital magnetic moment;b) spin magnetic moment.

    4. Atoms in a constant magnetic field:a) Larmor precession;b) Larmor precession frequency;c) Land factor.

    5. Effect of a magnetic field on the wave functions and energy levels of an atom.6. Normal Zeeman effect:

    a) Zeeman singlet splitting;b) Bohr magneton;c) selection rules for ;d) separation of Zeeman sublevels.

    7. Lorentz's theory:a) and components of Zeeman singlet splitting;b) polarisation of and components;c) Lorentz triplet.

    8. Anomalous Zeeman effect:a) anomalous Zeeman effect energy level splitting;b) Land factor.

    9. Experimental setup for the study of the transverse and longitudinal Zeeman effect.10.The construction and use of a Fabry Prot interferometer.11.Definition of polarised light.12.Using waveplates to change the polarisation of light.13.Interference filter parameters.

    II.Experimental tasks.1.

    Familiarise yourself with the experimental setup shown in Picture 1.

    2. Prepare the experimental setup to study the Zeeman effect. To do this, follow these steps:ensure that the transformers current knob (5,Picture 1)is set to position 0and then turn on

    the power to the transformer and cadmium lamp (3,Picture 1)(their switches are on the rear

    of the housings). Turn on the ammeter (6 in Picture 1).

    The digital meter shuts down automatically after a certain period of inactivity.

    Ensure that the ammeter remains on during measurements, turning it on again if

    necessary.

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    Experiment30: Normal and anomalous Zeeman effect

    Turn on the computer and start the CCD camera preview (follow the instructions inAppendix

    A).

    3. Record the red cadmium line (= 643,847 nm) splitting in the normal Zeeman effect.To do this, ensure that the magnetic field is perpendicular to the optical axis (the swivel table

    with electromagnet can be unlocked using the screw underneath).

    Place the red filter (7,Picture 1)in the interferometer slit and set the analysers orientation (1,

    Picture 1)to vertical.4. Gradually increase the current flowing through the coil of the electromagnet

    (with the knob on the transformers front panel 5,Picture 1)until splitting interference fringes

    are visible.

    5. Record images using the CCD camera (followingAppendix A) while increasing the current insteps of 1 A.

    6. Change the orientation of the analysers polarisation to horizontal and record images whilechanging the magnetic field strength.

    7. Using the electromagnet characteristics sheet inAppendix C,measure the magnetic fieldstrength for each value of the current .

    8. Analyse the results of measuring the Zeeman effect:a) UseAppendix Bor the instructions for the CCD camera control software (part 11. in IV.) to

    measure the interference rings on the recorded images;b) Plot a graph of the ratio /as a function of magnetic field strength ;

    Picture 1. Experimental setup for studying the Zeeman effect: 1 optical bench including (from left to right): CCD

    camera (in mounting), lens +50 mm, analyser, waveplate bracket, green filter bracket, lens +300 mm, Fabry

    Prot interferometer (with red filter holder), lens +50 mm; 2 swivel table with electromagnet and cadmium

    lamp; 3 lamp power supply; 4 capacitor; 5 transformer; 6 digital multimeter (ammeter); 7 accessories

    (from left to right):green filter in bracket, red filter, quarter waveplate in bracket; 8 computer.

    Do not exceed a current of 9 A through the electromagnet coils. To prevent

    overheating, turn the transformers current knob to minimum after completing

    the tasks.

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    Experiment30: Normal and anomalous Zeeman effect

    c) Calculate the Bohr magneton and electron specific charge =/(includinguncertainties);

    d) Compare your results with the data given in the literature.9. Explain the interference images in II.6.10.Record the cadmium spectral line splitting (= 508,588 nm) for the anomalous Zeeman effect.

    Ensure that the magnetic field is perpendicular to the optical axis.

    Remove the red filter from the Fabry Prot interferometer.

    Insert the green filter (7,Picture 1)in its mounting (1,Picture 1)(possible reflections in the

    preview from the CCD camera can be eliminated by gently rotating the filter in the horizontal

    plane).

    To make measurements of the component of the emitted light, orient the analyser (1,Picture

    1)vertically.

    11.Increase the current through the electromagnet until splitting interference fringes are visible.12.Record CCD camera images depending on the electromagnet current. Increase the current in

    steps of 0,5 A.

    13.Re-orient the analyser in the horizontal direction and repeat measurements for the component.

    14.Read off the magnetic field strengthfor each value of the currentin step II.12. inAppendixC.

    15.Analyse your results of measuring the anomalous Zeeman effect:a) measure the interference rings in your images of the anomalous Zeeman effect;b) Plot a graph of the ratio /as a function of magnetic field strength for the and

    components of the lamps spectral lines;

    c) Calculate the Bohr magneton and electron specific charge =/separately for bothcomponents of emitted light;

    d) calculate the average value of Bohr magneton and the specific charge of the electron andcompare them with the data found in the literature.

    16.Record interference fringes of the normal and anomalous longitudinal Zeeman effect.To do this, change the orientation of the electromagnet by turning the table so that the

    direction of the magnetic field is parallel to the direction of the light from the lamp.

    17.Select an appropriate filter for the type of Zeeman effect you would like to study.18.Place a quarter-wave plate in the holder (1,Picture 1).19.

    Set a coil current to give a sharp interference pattern on the screen.

    20.Record interference images for both Zeeman effects for two analyser orientations i.e., +45 and-45 relative to the vertical axis.

    21.Develop a conclusion from the results of your analysis.

    III.Apparatus.1. CCD camera.2. 2 lenses +50 mm.3. 1 lens +300 mm.4. Analyser.5. Fabry Prot interferometer (etalon size 310-3 m).

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    Experiment30: Normal and anomalous Zeeman effect

    6. Green filter (= 508 nm) in housing.7. Red filter (= 595 nm) in housing.8. Quarter-wave plate.9. Cadmium lamp.10.Electromagnet.11.Cadmium lamp power supply.12.Transformer.13.Swivel table.14.Capacitor with capacitance of 22 mF.15.Universal multimeter.16.Computer with Motic Image Plus 2.0 ML software program.

    IV.Literature.1.

    PHYWE Laboratory Experiment Physics, 5.1.10-05 Zeeman Effect, www.phywe.com.

    2. E.U. Condon & G.H. Shortley The Theory of Atomic Spectra, Athenaeum Press Limited,Newcastle upon Tyne 1991.

    3. H.A. Enge, M.R. Wehr, J.A. Richards Introduction to Atomic Physics, Addison-Wesley,Reading-Mass, 1981.

    4. W.A. Shurcliff, S.S. Ballard Polarized Light, Princeton, N.Y. 1964.5. V. Acosta, C.L. Cowan, B.J. Graham Essentialsof Modern Physics, Harper & Row, N.Y. 1973.6. H. Haken, H.Ch. Wolf The Physics of Atoms and Quanta, Springer, 2000.7. R.P. Feynman, R. Leighton, M. Sands The Feynman Lectures on Physics, Vol. II, Part 2 &

    Vol.III., Addison - Wesley, 2005.

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    Experiment30: Normal and anomalous Zeeman effect

    Appendix A

    Recording an image using the CCD camera and the Motic Images Plus 2.0 MLsoftware

    package

    A.Turning on and adjusting the CCD camera preview.1. Star the program Motic Images Plus 2.0 MLby clicking on the desktop icon (or

    the start menu).

    2. The program main window will open:

    3. Click the camera icon located on the upper toolbar (seePicture 2).The Motic Live Imaging Modulewill open with a camera preview (Picture 3).

    Picture 2. Motic Images Plus 2.0 ML main window: 1 preview of the currently edited image, 2 toolbar, 3

    thumbnail list of captured images. Currently selected image is outlined in red.

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    4. Use the bookmark panel icons (1,Picture 3)to view the different configuration options, makingchanges if needed (2,Picture 3), including brightness, colour saturation, contrast, sharpness,

    etc.

    B.Recording images from the CCD camera.1. Click the camera icon in the Motic Live Imaging Modulebookmarks panel (1,Picture 3).2. Select the output image resolution from the Formatdrop-down list. It is advisable to store

    images in the greatest possible resolution for easier processing.

    3. Click Captureto capture an image from the CCD camera.4. A thumbnail will appear in the Motic Images Plus 2.0 MLthumbnail panel (3,Picture 2). By

    clicking on the desired thumbnail you can view a full preview of the captured image (1,Picture

    2).

    Picture 3. Motic Live Imaging Module window: 1 bookmarks panel; 2 configuration panel; 3 camera

    preview panel.

    Customizing the CCD camera preview options can improve image clarity. A

    particularly useful option is digital noise reduction (Remove Noise).

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    5. Captured images are stored in the folder Capture Folderwhich has a shortcut on the desktopand start menu. The program saves images in its own SFC format by default. To process them in

    another program, save them asJPEGor TIFF. To do this:

    a)

    click the thumbnail in Motic Images Plus 2.0 ML;b) when it appears in the preview panel (1, Picture 2), click Fileand choose Save As;c) in the next window, enter the name of the selected image, select the file format, specify

    the folder where the image is to be saved and click OK.

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    Appendix B

    Making distance measurements from CCD camera images using the program NI Vision

    Assistant 2009(for example, interference fringes)

    A.General information.The software program National Instruments Vision Assistant offers the ability to take measurements

    of geometrical properties of objects shown in raster images, such as distances between points, areas,

    diameters, etc. The program supports most of todays popular formats (including *.bmp, *.jpg, *.tif,

    *.png).

    A List of operations performed sequentially by NI Vision Assistant, such as image transformations,

    distance measurements and conversions is written in a script that appears in the script editing panel

    (4,Picture 4).

    Each step in the current script may be deleted by clicking on the icon, or edited by clicking on

    or double-clicking on the icon representing a step.

    B.Opening and preparing their images for editing.1.Open a picture (pictures) in NI Vision Assistantin one of two ways:

    Picture 4. NI Vision Assistant program window: 1 function selection panel; 2 image selection panel; 3 image

    preview panel; 4 script editing panel.

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    a) click the button on the toolbar of the main window (or select Open Imagein the Filemenu), and then select the image (images) and click Open;

    b) go to the image viewer, click Browse Imageson the right of the toolbar in the main window,click at the bottom of the screen, select the images and click Open.

    2.After opening the desired image (images), you can start editing them and makingmeasurements. All operations are found on the image processing tab, accessible by clicking

    Process Image, located on the right of the toolbar in the main window.

    3.At any time, you can select which image to edit with the Process Image tab by clicking inthe image selection panel (2, Figure 4), or by going to the browser (click Browse Images) and

    double-clicking the selected thumbnail image (or selecting the thumbnail with a single mouse-

    click and going to the Process Image tab).

    4.To add new images to the browser, click at the bottom of the screen, then select the image(images) and click Open.Depending on the preferences, a dialogue box will appear askingwhether you would like to replace the existing images with the newly selected images.

    5.Clicking in the image viewer allows you to switch between a grid view of thumbnails or asingle image.

    C.Measuring distances between two points.The program NI Vision Assistantallows you to measure distances between points on images,

    transforming the distance in pixels into a distance expressed in physical units. To do this, you have to

    calibrate the image.

    Image calibration.

    1. Select Image Calibration from theImagemenu. The calibration wizard window will appear.2. Ensure that the first option is selected - Simple Calibration. Click OK.3. In step 1 (Step 1 of 3) you will see a preview of the currently open image.

    Ensure that you select square pixels (Square), and click Next.

    If after opening, the image (images) appear completely black, you must convert

    the file by changing its bit-depth. To do this:

    1. select the appropriate image and go to the edit tab (Process Image);

    2. under the Greyscalemenu, select Conversion, and in the function selection

    panel (1, Figure 4), choose 8-bit [0, 255]and confirm by clicking OK.

    The converted image can be saved by clicking Save Imagefrom the File menu.

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    4. In step 2 (Step 2 of 3), select two points on the image separated by a known actual distance(e.g., two points on the centimetre scale on the image screen), clicking on the appropriate

    points in the preview.

    In the numeric field in the section Correspondence Image Real World, enter the physicaldistance between the selected points and select the appropriate unit (see Picture 5).

    Picture 5. Calibration wizard for the program NI Vision Assistant (image preview with two points separated by a known

    physical length (1 cm))

    5. After setting the reference distance, click Nextand then OK. The calibration wizard will close.6. Confirm the image calibration data by clicking OKin the function selection panel (1, Picture 4).Measuring distances on images

    1. After image calibration, you can make distance measurements between any two points. To dothis, click Measure in the function selection panel (1,Picture 4):

    2. Select Length from the list of possible measurements in the function panel (titled MeasureSetup).

    3. Use the mouse to select the two end points of the segment for the distance you wish tomeasure.

    The length of the segment in physical units will be displayed in the table of measurements inthe script editing window (Length = ).

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    Experiment30: Normal and anomalous Zeeman effect

    4. A series of distance measurements can be made by drawing new segments. Each newmeasurement will be stored on a separate line in the table.

    5. Collected data can be saved as a text file or put in a spreadsheet in Microsoft Excel. To do this,click one of the buttons on the right-hand side of the script editing panel (Save Resultsor SendData To Excel). The resulting file can then be imported into any program used for processing

    and visualising numeric data (e.g.: Origin, Sigma Plotamongst others).

    6. To exit the Measure tool, click OKin the Measure Setup panel.You can always go back to the results of your measurements (or take more), by double-clicking

    the Measureicon in the script editing window.

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    Appendix C

    Dependence of magnetic field strength on current through the electromagnet coils in the

    experiment for studying the Zeeman effect (for a pole separation distance of 9 mm)

    Source: Opis ukadu pomiarowego nr P251105, PHYWE Systeme GmbH & Co. [11]