Dispersion of Glass Introduction This experiment will develop skills in aligning and using a spectrometer to measure dispersion of glass, and choosing a suitable fit for data and plotting the resulting curve. Curve fitting will count for a big chunk of the marks in this lab, so don't try to avoid it! Apparatus - Spectrometer, - Bubble Level, - 60 o Prism, - Small Allen wrench, screwdriver, - Sodium Lamp, - Hydrogen, Helium and Mercury Geissler Tubes with Power Supply, - Assorted stands and clamps. Theory In this experiment we shall use the angle of minimum deviation to measure the index of refraction of glass as a function of wavelength. When a ray of light is obliquely incident on the interface separating two transparent media of different indices of refraction, its direction changes. The amount of deviation is described by Snell's Law: n sinθ = n sinθ () where n is the index of refraction of medium,θ is the angle of incidence (measured from the normal to the interface), n is the index of refraction of medium, andθ is the angle of refraction. For most transparent media, the angle of refraction increases with increasing frequency (for a fixed angle of incidence) thus, blue light is refracted through a much larger angle than red light. Furthermore, the index of refraction of a material is not a constant, but depends upon the frequency of the incident light. From measurements of the index of refraction of a medium as a function of wavelength, we can construct a dispersion curve by plotting a graph of n vs.λ. The dispersion of the medium at a particular wavelength D is defined to be the slope of the dispersion curve at that wavelengthλ 0. d n D = ( ) λ0 () dλ Referring to Figure, when a ray of monochromatic light passes through the prism, it is deviated through some angle. The value of this angle depends on the angle of incidence at the first surface of the prism. When the angle of incidence θ i is equal to the angle of emergenceθ e, the angle of deviation is a minimum, called the angle of minimum deviation min.
Figure : Path of light through a prism in air The index of refraction of the glass, n, can then be found from: n = n sin[( α+ min ) sin( α / ) / ] (3) Where αis the prism angle, n is index of air. Procedure. Aligning the Spectrometer See the appropriate section on the course web site.. Measurement of Prism Angleα Figure : Orientation of prism to find prism angleα
Place the prism on the prism table with the prism angle pointing toward the collimator as in Figure. Place a light source in front of the collimator. Use a narrow collimator slit in the following procedure. Note that the slit image can be seen reflected in the prism faces. Adjust the telescope so that the slit image is aligned with the cross hairs, read the vernier scale (30 part vernier every half degree; thus readings are in degrees and minutes), and record this reading (the telescope angle). Be as careful as possible when taking measurements, and be sure to record values to the nearest minute of angle. Sloppy measurements will give you meaningless results. Repeat this for the other prism face and enter your readings into Table. Repeat these measurements 3 times. The prism angle is one half the difference between the two vernier readings. From the three series of measurements recorded in Table, determine the prism angle αfor each measurement, and calculate the average value of the prism angle. Include measurement uncertainties in your final answer. Table : Calculation of Prism Angle Trial # Left Reading Right Reading Prism Angle α 3 3.Measuring the Angle of Minimum Deviation min Place the sodium vapour lamp in front of the collimator slit. Rotate the prism so that now light will be refracted through it on the way to the telescope. Observe the spectral lines and reduce the slit width until they are sharp and narrow. Read and record the left and right readings of the slit L and R with no prism on the prism table. Place prism on the table and line up one spectral line with cross hair. Rotate the prism table as shown in Figure 3 toward the direction of incident light. When the spectral line seen in telescope suddenly moves in opposite direction line up the line with cross hair by rotating the table back. Record the left and right readings of vernier L and R for the spectral line in Table. The angle of minimum deviation is achieved by the following expression: = (4) 0L L L = 0R R R (5) min = 0L + 0R ( = L R ) + ( R L ) (6) ( lines separated by 6 A ; these may be too close together to be clearly resolved, if so, set the cross hairs to the center of the doublet and use the mean wavelength of 5893 A.) Record the vernier reading in Table. Repeat this measurement three times. If you have any difficulty, see the laboratory demonstrator. Q: How do you determine the uncertainty in the average of a set of numbers? The difference between the vernier readings from each side is twice the angle of minimum deviation.
Repeat using the Hydrogen Geissler tube and the four visible lines of the Hydrogen spectrum (red, blue and two violet). Figure 3: Rotating prism table to find the angle of minimum deviation min Repeat using the Mercury Geissler tube and as many as possible of the following lines of the Hg spectrum: two close yellow lines separated by 0 A; two greens; a blue-green; and a blue (this is a triplet - use the center of the image). Repeat using the Helium Geissler tube and any 4 visible lines. Table : n vs wavelength Colour Wavelength L R L R 0L 0R min n H (r) Na (y) Hg (y) Hg (y) Hg (g) Hg (g) H (b-g) Hg (b-v) H (v) H (v) Hg (v) Hg (v) He (y)? He (g)? He (b-g)? He (b-v)? 6563 5893 5790 5770 546 505 486 4358 4300 40 4077 4047
B(blue); g(green); r(red); v(violet); y(yellow) (colours are approximate.) Result Analysis and discussion. Plotting the Dispersion Data Using the angles of minimum deviation for each wavelength measured, along with their uncertainties, and the average value of the prism angle α, along with its uncertainty calculated above, determine the index of refraction at each wavelength, along with the uncertainties, and place them in Table.. Plot a graph of n vs.λ. If your graph does not suggest a smooth, monotonically decreasing function, go back and check your data. Bad data will make your results meaningless.. Curve Fitting This is the most important part of this experiment. Don't try and take shortcuts in this section. For each of the following fits, do the fit and determine A, B, and C (if applicable). Make a table of these results including the SSE for each fit. Determine which of the following functional forms best approximates your dispersion curve: n = A + B/λ n = A + B/λ n = A + /(λ-b) n = A + B/λ+C/λ n = A + B/λ +C/λ 4 n = A + B/(λ-C) Note that two of the above fits are non-linear, and will force you to use the optimizer. You'll also need to come up with reasonable starting values for the optimizer. This will take time, but that's why this part of the lab will carry a lot of marks. 3.Extracting Information from the Graph After finding the best fit to the data, draw the best fitting smooth curve through the data points. From your dispersion curve, determine the index of refraction of the glass for the Fraunhofer F, C and D lines whose wavelengths are 486A o, 6563A o and 5893A o, w = n n F C n D (7) respectively. Using this information, calculate the dispersive power W of the prism from Determine the unknown wavelengths of the 4 Helium lines from your dispersion curve, using the solve for spreadsheet function and determine uncertainties appropriately. Compare your results with the accepted values found in the C.R.C. Handbook.