# Studies of a Diffraction Grating, Spectral Lines of Hydrogen, and Solar Spectrum

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1 Studies of a Diffraction Grating, Spectral Lines of Hydrogen, and Solar Spectrum Objectives: 1. To become familiar with capturing spectral lines using a CCD camera. 2. To study selected properties of a diffraction grating. 3. To study the Balmer series of hydrogen. 4. To resolve the red spectral lines of hydrogen and deuterium. 5. To observe the absorption lines sodium, and calcium in the solar spectrum. Apparatus: Hydrogen lamp, deuterium lamp, sodium lamp, slide projector (as a white light source), beam splitter, He-Ne laser ( λ = 632.8nm ), variable slit, convex lenses (f =10 cm, 12 cm and 25 cm), prism, diffraction grating (~1000 lines/mm), monochromator, CCD camera, PC, black cardboard boxes. Part 1 Studies of a diffraction grating Introduction (Reference: Hecht, Optics) The key component of a monochromator a grating or two or even three gratings. When you look at the specification of a grating, you often see Blazed at xxx nm. Here, we briefly describe this important type of gratings. The reason for using a blazed grating design is to concentrate optical energy at a certain order. For common gratings the grooves looks like so that optical energy will, after reflecting from the grating, distribute more or less evenly among several orders, which is certainly undesirable. A blazed grating is used inside a high-end monochromator, shown in the diagrams below: γ γ mth order b a θ i γ θ r Specular b 2γ =θ r 2γ =θ r Normal to plane of grating Fig. 1-1(a) Section of a blazed grating. 1 Fig. 1-1(b) Condition for desired order.

2 Such an objective is achieved for specular reflection, i. e. θ i = 0; θ r = -2γ asin(-2γ) = mλ ; γ is the blaze angle, m is the desired order. The convention is that θ r is negative if θ i and θ r are on the same side of the normal to the plane of grating. Procedures: 1-1. Use the slide projector to form a beam an essentially plane wave of white light to incident on a blazed grating. Use the digital camera provided to record the images of the diffraction patterns (projected on a white screen) at several incident angles Analysis of the diffraction pattern obtained. Part 2 Spectral lines of hydrogen Background: Balmer examined the four visible lines in the spectrum of the hydrogen atom. Their wavelengths are 410 nm, 434 nm, 486 nm, and 656 nm. He played around with these numbers and eventually figured out that all four wavelengths λ fit into the equation R( ) 2 2 λ = 2 n, where R is the Rydberg constant (value m -1 ). This set of lines is called the Balmer series. Later, other researchers found that the series could be extended into ultraviolet wavelengths. The same formula still works, with larger values of n. From Balmer s equation, it is clear when n gets larger, the lines are getting closer together. The accepted values of the Balmer series (in air) are listed below: Table 1 Balmer Series Balmer Series (blue and violet regions) Wavelength (nm) Relative Intensity n Color or region UV UV UV Violet Violet Violet Blue 2

3 Experiment setup: Hydrogen Lamp f=12cm f=25cm Beam splitter slit prism f=10cm CCD He-Ne laser ( λ = 632.8nm ) PC Fig. 2-1 Experimental setup. Procedures: 2-1. Set up the experiment as shown in Fig Align the optical components till the light from the hydrogen lamp and the laser beam go through the same light path. It is easier to align the system by observing the laser beam path (Another use of the laser beam is as a wavelength reference). Also make sure that the prism is at the minimum deviation and the light spot is well focused on the CCD chip Observe the spectra lines on the PC screen and find the hydrogen lines listed in Table 1 by using the laser spot as a reference Carefully adjust the distance of the CCD and the lens until the first two lines (i.e and/or nm) are best focused. Record the image by using a proper exposure time (to see the faint spectral lines at shorter wavelength a large enough exposure time ~20 second or more is needed) and save the image Repeat 2-4 until the last few lines are focused well and record another image. Note: In order to record good images and the faint spectral lines (e.g nm) of hydrogen, a black card box is needed to block stray light, so that large enough exposure time, say 20 second or larger can be used. Requirements and Information for data analysis: 1. It is well known that refractive index of dielectric material, such as glass, is a function of wavelength, which is given, to a good approximation, by, Cauchy equation n A B λ 2 g = + /, where n g is the refractive index, both A and B are constant for a given substance and λ is the wavelength. From this equation, with relative small difference of wavelength, there will be a slightly larger separation of the spectra lines in the shorter wavelength region because of larger dispersion. Actually, this was observed in the experimental results. a) Assume that the angular position of the spectra line is proportional to its n value (in fact, a good approximation). Because n= Kθ and θ d, where d is the position of spectral lines, 3

4 the relationship of d and λ is then: md A B λ 2 = + /, where m is an integer. Let m = 1, Assume that two spectral line are exactly equal to their accepted values and use Cauchy s equation to obtain A and B and thus the values of the other spectral lines. Part 3 The red spectral lines of hydrogen and deuterium Background: The basic grating equation is sinα + sinθ = mnλ, whereα is the angle between the incident light and the normal to the grating, θ is the angle between the diffracted light and the normal to the grating, m is the order number and n is the number of grooves per millimeter. When a parallel beam of polychromatic light is incident on a grating then the light is dispersed so that each wavelength satisfies the grating equation. As a result, blazing grating is often used to analyze atomic spectral lines. The energies of corresponding levels in hydrogen and deuterium differ by approximately 0.25 % because of the different reduced masses of these two atoms. Precise measurements of Balmer emission spectra for these atoms suggested that the red lines of hydrogen and deuterium are at nm and nm, respectively. In this experiment, the spectral lines of hydrogen and deuterium will be observed and their two red spectral lines will be recorded and analyzed. Experimental setup: White Screen Hydrogen lamp Slit ~13m Blazing grating Beam splitter Deuterium lamp He-Ne laser (for alignment) Lens (f= 50cm) CCD camera PC Fig Experimental setup. Procedures: 3-1. Set up the experiment as shown in Fig Align the components till the reflected light from the white screen and the laser beam passes through the same optical path. It is easier to align the system by observing the laser beam path Adjust the position of the CCD camera such that the laser spot can be clearly seen on the PC screen. Then slightly move the CCD camera toward or away from the lens so that the laser spot was well focused on the CCD screen Block off the laser beam and unblock the two spectral lamps First identify, roughly, the position of the hydrogen and deuterium read lines by bare eye by looking into the lens Put the CCD to the place identified by eyes where red spectral lines can be observed. Carefully adjust the distance of the CCD and the lens until the two red lines from the two lamps 4

5 are best focused. Record the image by using a proper exposure time (~800 ms or more if needed). Block the light from the slit and record another image as the background. Requirements: Image of the two red spectral lines. Estimated FWHM of the spectral lines. Estimated spectral resolution of the system. Part 4 Studies of the solar spectrum Background: The solar spectrum is a continuum spectrum with thousands of dark absorption lines superposed on it. These lines are called the Fraunhofer lines, and the solar spectrum is sometimes called the Fraunhofer spectrum. These lines are produced primarily in the photosphere of the sun. And the following table is a list of the most prominent Fraunhofer lines. Table 2. A list of the most prominent Fraunhofer lines Lines Due To Wavelengths (nm) A - (band) O B - (band) O C H 6563 a - (band) O D - 1, 2 Na 5896 & 5890 E Fe 5270 b - 1, 2 Mg 5184 & 5173 c Fe 4958 F H 4861 d Fe 4668 e Fe 4384 f H 4340 G Fe & Ca 4308 g Ca 4227 h H 4102 H Ca 3968 K Ca 3934 In this part of the experiment, part of the solar spectrum that contains the D-1, 2, (and possibly calcium line near nm, and the hydrogen line near nm) Fraunhofer lines will be recorded. Note: in an emission spectrum, this pair of intense yellow lines (wavelengths of and nm) is the most significant feature of the sodium spectrum. 5

6 Experimental setup: Sunlight White screen Monochromator ~15cm Entrance slit L1, F=15cm ~10cm Sodium lamp Exit ~27cm L2, F=10 cm ~16cm PC CCD camera Fig. 4-1 Experimental setup. Procedures: 4-1. Set up the experiment as shown in Fig Align the system to make sure that: (a) The sunlight as well as the sodium lamp properly light the white screen put near the window. (b) The incident light of the monochromator is normal to the entrance slit so that the incident light can be cast on the concave mirror in the monochromator properly. (c) Use a black card box to block the stray light so that long exposure time can be used Turn on the sodium lamp and use a large slit (~1 mm) first so that it is easy to align L1, L2 and the CCD. Adjust the monochromator to the wavelength of ~595 nm and then slightly move the CCD closer (or further) to the lens till sharp sodium lines (the double lines of and nm) appear on the computer screen Adjust the entrance slit to about 0.1 mm and use an appropriate exposure time so that sharp sodium lines appear on the computer screen without over exposed Block the sodium lamp and increase the exposure to about 20 s, record the image when two sharp dark lines at the same positions of those of the double sodium lines can be seen on the computer screen (Proc. 4-4). Requirements: Image of the sodium absorption lines. Fraunhofer spectrum of the region that you have recorded (light intensity versus wavelength). You abundance of elements (that is larger than %) on the surface of the sun is listed in the Appendix. Try to reconstruct the Fraunhofer lines near the spectral region(s) that you have recorded. (Use the information available on the Web site: 6

7 Appendix 1 Data Processing -- Extracting the Spectra You have to use the PC connected to LAN in Rm 115) A1-1. A1-2. Use Photoshop to open the data file (in JPEG format) to be analysed. If the Raman lines are not exactly vertical, rotate the image such that they are. A1-3. Click the icon once and then point the mouse to the picture to select, say, ~200 lines of pixels. A1-4. Invoke File and then select New. A1-5. Invoke Edit and then Paste the selected portion to this new file. A1-6. Save this new file with a name that you like (say yyyy) with an extension.raw. A1-7. Minimize Photoshop and then double click the icon Labview. A1-8. Several choices should appear on the screen. Select Open Vi and then select Programs and then Main and eventually Convert.vi A1-9. When Convert.vi is running, you can click the Load button once and load the file yyyy.raw. Then signal averaging will be carried out with a spectrum appear on the PC monitor. A1-10. Click the save button to save the result in ASCII format with an extension.dat Appendix 2 UV105 and UV107 Exposure Time Control Function Keys F1 through F8 are used to select or modify exposure times F1 <shift> F1 F5 <shift> F5 F6 <shift> F6 F7 <shift> F7 F8 sets the exposure time to the default exposure time of 100 milliseconds. prompts the user to enter a new exposure time in milliseconds. increments the present exposure time by 1 second. decrements the present exposure time by 1 second. increments the present exposure time by 0.1 second. decrements the present exposure time by 0.1 second. increments the present exposure time by 0.01 second. decrements the present exposure time by 0.01 second. increments the present exposure time by 1 millisecond. 7

8 <shift> F8 decrements the present exposure time by 1 millisecond. Appendix 3 UV105 and UV107 Single Key-Stroke Commands Commands which control camera operation (a)nti-blooming (i)nterlace (l)ive camera image Toggles anti-blooming mode off for highest dynamic range, and on for blooming reduction and lower dark current. Available only when image is live. Toggles interlace mode on and off (available only when image is live ). Two separate image frames are required for each interlaced image. Toggles live camera image mode on and off. Utility Commands (b)ias (h)elp (p)cx (q)uit (t)iff Displays a numerical indication of image brightness. Three numbers are displayed: the minimum brightness level, the mode of the brightness levels, and maximum brightness level. Displays help screens. Saves current image as a PCX file. The user is prompted for the name of the PCX file to be created. Terminates UV105 or UV107. Saves current images as a TIFF (Tag Image File Format) file. The user is prompted for the name of the TIFF file to be created. 8

9 Appendix 4 Element Atomic Abundance (%) Element Atomic Abundance (%) Number Number 9

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