PH2 page 1 DISPERSION OF A GLASS PRISM OBJECTIVE The objective of this experiment is to analyze the emission spectrum of helium and to analyze the dispersion of a glass prism by measuring the index of refraction for different colours in this spectrum. INTRODUCTION Light is emitted or absorbed when electrons change their orbit within an individual atom. Therefore, a spectrometer can be used to investigate the structure of atoms and also to determine which atoms are present in a substance. In this experiment a spectrometer will be used to examine the visible spectrum emitted by helium in a discharge tube and to determine the index of refraction of a glass prism as a function of the wavelength and the associated dispersion. In principle, a spectrometer is a very simple scientific instrument: It can bend a beam of light with a prism. If the beam is composed of more than one color of light, a spectrum is formed, since the various colors are refracted to different angles. The result is a spectral "fingerprint," which carries a wealth of information about the substance from which the light is emitted. In its simplest form, a spectrometer is nothing more than a prism and a protractor. However, because of the need for very sensitive detection and precise measurement, a real spectrometer is a bit more complicated. As shown in Figure 1, a spectrometer consists of three basic components; a collimator, a prism, and a telescope. Adjustable Collimator Slit Collimator A Prism Angle of Deviation Telescope Light Source Eye Piece Figure 1. Spectrometer Diagram The light to be analyzed enters the collimator through a narrow slit positioned at the focal point of the collimator lens. The light leaving the collimator is therefore a thin, parallel beam, which ensures that all the light from the slit strikes the prism at the same angle of incidence. This is necessary if a sharp image is to be formed. The prism bends the beam of light. If the beam is composed of many different colours, each colour is refracted to a different angle. The telescope can be rotated to collect the refracted light at very precisely measured angles. With the telescope focused at infinity and positioned at an angle to collect the light of a particular color, a precise image of the collimator slit can be seen. For example,
PH2 page 2 when the telescope is at one angle of rotation, the viewer might see a red image of the slit, at another angle a green image, and so on. By rotating the telescope, the slit images corresponding to each constituent color can be viewed and the angle of refraction for each image can be measured. Slit Image Slit Image Vertical Cross-Hair Vertical Cross-Hair Figure 2. Telescope View at Different Angles If the index of refraction of the prism for each colour in the light is known, then these measured angles can be used to determine the wavelengths that are present in the light. However, if the wavelengths of the colours in the light are known, then the measured angles can be used to determine the index of refraction of each colour. For a prism, the angle of refraction is not directly proportional to the wavelength of the light. The Angle of Minimum Deviation The angle of deviation for light traversing a prism is shown in Figure 3. For each wavelength of light traversing a given prism, there is a characteristic angle of incidence for which the angle of deviation is a minimum. Figure 3: Reading the Angle of Deviation This angle depends only on the index of refraction of the prism and the angle (labeled A in Figure 3) between the two sides of the prism traversed by the light. The relationship between these variables is given by the equation: (Eq. 1) where n is the index of refraction of the prism for a given wavelength; A is the angle between the sides of the prism traversed by the light; and D min is the angle of minimum deviation. Since n varies
PH2 page 3 with wavelength, the angle of minimum deviation also varies, but it is constant for any particular wavelength. EQUIPMENT The spectrometer includes the following equipment: Prism Figure 4. The Spectrometer Collimator and Telescope Both the collimator and the telescope have 178 mm focal length, achromatic objectives, and clear apertures with 32 mm diameters. The telescope has a 15X Ramsden eyepiece with a glass, cross-hair graticule. The collimator is fitted with a 6 mm long slit of adjustable width. Both the collimator and the telescope are aligned so that their optical axes are perpendicular to their axis of rotation. Rotating Bases The telescope and the spectrometer table are mounted on independently rotating bases. Vernier scales provide measurements of the relative positions of these bases to within 20 minutes of arc (or 0.1 degree of arc depending on the model; see the two examples reading the vernier below). The rotation of each base is controlled with a lock-screw and fine adjust knob (see figure 4 above). With the lock-screw released, the base is easily rotated by hand. With the lock-screw tight, the fine adjust knob can be used for more precise positioning. Spectrometer Table The spectrometer table is fixed to its rotating base with a thumbscrew, so table height is adjustable. Three leveling screws on the underside of the table are used to adjust the optical alignment. (The table must be level with respect to the optical axes of the collimator and telescope if the prism is to retain its alignment for all positions of the telescope.) Thumbscrews are used to attach the prism clamp and the grating mount to the table, and reference lines are etched in the table for easy alignment.
PH2 page 4 PRELIMINARY ADJUSTMENTS The spectrometer may need adjusting before being used. The purpose of these preliminary adjustments is to get parallel rays to pass from the collimator through the prism and to the telescope. FOCUSING THE SPECTROMETER The next three steps of the adjustments must be carried out in the order indicated. Once completed properly, these adjustments should not need further attention for the duration of the experiment. (a) ADJUSTMENT OF THE CROSS-HAIRS While looking through the telescope, slide the eyepiece in and out until the crosshairs come into sharp focus. Loosen the graticule lock ring, and rotate the graticule until one of the cross-hairs is vertical. Retighten the lock ring and then refocus if necessary. (b) ADJUSTMENT OF THE TELESCOPE Point the telescope toward a distant object. Adjust the focusing screw until the distant object is seen clearly. There should be no parallax between the cross-hairs and the image of the distant object. (c) ADJUSTMENT OF THE COLLIMATOR The collimator resembles the telescope except it carries an adjustable slit at one end. Place a light source close to the slit. Turn the telescope into line with the collimator as in Figure 5. Looking through the telescope, adjust the focus of the collimator and, if necessary, the rotation of the telescope until the slit comes into sharp focus. There should be no parallax between this image of the slit and the cross-hairs Do not change the focus of the telescope.. Figure 5: Alignment of the Telescope directly opposite the Collimator Tighten the telescope rotation lock-screw, then use the fine adjust knob to align the vertical line of the graticule with the fixed edge of the slit. If the slit is not vertical, loosen the slit lock ring, realign the slit, and retighten the lock ring. Adjust the slit width for a clear, bright image. Measurements of the refraction angle are always made with the graticule line aligned along the fixed edge of the slit, so a very narrow slit is not necessarily advantageous.
PH2 page 5 READING THE VERNIER SCALE EXAMPLE 1 The vernier in this example will allow you to read the angle to the nearest half a minute. Observe that the main scale divides one complete a revolution into 360. Each degree on the main scale is in turn divided into three parts (20 minutes each) or two parts (30 minutes each) depending on the spectrometer type. The sliding scale (or the vernier) is used to measure to the nearest minute or better. The vernier scale will thus have either 20 or 30 major divisions, and perhaps in between divisions indicating half minute readings. The divisions of the vernier scale are arranged such that at any given time only one of the divisions will be usually perceived as being closest to the perfect alignment with a main scale line. The exception being the first and last vernier lines which can both align with the main scale at the same time. To take a reading, first take the main scale reading immediately bellow the position of the zero line of the vernier scale. This main scale reading will be a multiple of 20 minutes (or 30 minutes for some spectrometers). The vernier scale is then read noting which line on the vernier scale most closely aligns with a main scale line. The vernier scale reading is then added to the main scale reading. Figure 5 shows an example reading with a vernier scale that is divided into twenty minute divisions with half divisions in between. The main scale reading is to 231 40, and the vernier scale reads 12.0. Thus the complete reading is 231 52.0. Closest to perfect alignment Figure 6: Vernier Reading Example 1 Main scale divides one complete revolution into 360 0 and the vernier has 20 major divisions with half divisions in between. In this example, the vernier line closest to perfect alignment with the main scale line reads 12 EXAMPLE 2 In this model, the main scale is divided into 360 0 and the vernier has 10 divisions. Therefore, you will be able to read the angle to the nearest 0.1 of a degree. Begin by reading the main scale directly below zero on the vernier scale: in the example in figure 6 below, this is 19 o ; use the next smallest number below the line pointed-to by the small red vertical arrow in figure 7 below. Next, the fractional part can determined using the vernier s auxiliary scale. Simply follow the lines across on the vernier scale (the outside scale) until you locate the only one which best lines-up with a line on the circular inner scale. In this example, the eighth line (corresponding to 0.8 o ) is best aligned with a line on the inner ring. On either side of this line (e.g. 0.7 or 0.9) you ll see that the lines do not match. Finally we add our integer angle of 19 o to our vernier reading of 0.8 o to get 19.8 o.
PH2 page 6 Closest to perfect alignment Figure 7: Vernier reading, Example 2 Main scale divides one complete revolution into 360 0 and the vernier has 10 divisions. The vernier line closest to perfect alignment with the main scale line reads 0.8 PROCEDURE: MEASURING THE ANGLE OF MINIMUM DEVIATION 1. Place the light source a few centimeters behind the slit of the collimator. 2. Once you have aligned and focused the spectrometer as described earlier, place the prism on the spectrometer table so that the incident light passes through it. It may be helpful to partially darken the room. 3. It is generally possible to see the refracted light with the naked eye. Locate the general direction to which the light is refracted, and then align the telescope and spectrometer table base so the slit image can be viewed through the telescope. 4. While looking through the telescope, rotate the spectrometer table slightly back and forth. Notice that the angle of refraction for the spectral line under observation changes. Rotate the spectrometer table until this angle is a minimum, and then rotate the telescope to align the vertical cross-hair with the fixed edge of the slit image as in Figure 8 below. Use the fine adjust knobs to make these adjustments as precisely as possible, then measure the telescope angle θ min using the vernier scale. Slit Image Vertical Cross-Hair Figure 8: View through the telescope
PH2 page 7 5. Without changing the rotation of the spectrometer table, remove the prism and rotate the telescope to align the cross-hair with the fixed edge of the unrefracted beam. Measure the angle θ on the vernier scale. The difference between this angle and that recorded for the refracted spectral line in step 4, is the angle of minimum deviation. Notice that, since the determination of the angle of minimum deviation for each spectral line requires rotational adjustments of the spectrometer table, the angle of the undeflected beam must be remeasured for each line. 6. The table below gives the wavelengths (in nm) of the spectrum lines that can be seen clearly in the helium discharge. Record in the same column, the values of the θ 0 (the vernier angle with the telescope and collimator axis aligned), θ min (the vernier reading at minimum deviation). Table of observations: Dispersion of Helium Light Through A Glass Prism. Colour of the Lines in the Helium Discharge Wavelength (nm) weak red 707 strong red 668 yellow 588 green 502 blue-green 492 blue 471 violet 447 A ( o ) θ 0 θ min D min = θ min θ 0 60 o 7. Repeat steps 3 to 5 above for five other lines of the spectrum and record your observations in the table above. DATA ANALYSIS 1. For each of the analyzed lines calculate the angle of minimum deviation D min, and then the index of refraction n, of the glass of the prism to four significant digits using the Eq. 1. Record your results in the table above 2. Using the values in this table, plot a graph of the index of refraction vs. the wavelength of these spectral lines. Analyze and comment on the shape of this graph. 3. Could you use this graph to predict the index of refraction of the glass prism for a different colour, not present in the current spectrum?