Experiment 1 Refraction by a Prism The first quantitative work on optics that is known was done by Ibn Al-Haytham circa 10281038. The first explanation of the rainbow was given by the Dominican monk Theodoric of Freiburg, (1250-1310). He used various crystals, water flasks and parchment with small holes. Some of the apparatus he used is still in existence. Preparation Prepare for this experiment by reading about index of refraction, Snell's Law, minimum angle of deviation, and chromatic aberration. Principles Light of all wavelengths travels through vacuum at the same velocity, c. When light enters another medium such as air, water, glass, or plastic, its velocity will be reduced. The index of refraction of light for a particular substance is defined as the ratio of the speed of light in vacuum to the speed of light in that substance, that is: c n= . v This ratio also depends on the wavelength of the light. It is more properly written n( λ ) . Textbooks often give a single value in tables of indices of refraction but they specify the wavelength for which the index was measured. According to Snell's Law, a beam of light that moves from one medium to another is bent toward or away from the normal according to n1 sinθ1 = n2 sinθ2 , where θ1 and θ2 are the angles of the light rays in the two media as measured from the surface normal. Assume that you have a prism of apex angle Φ . Assume that the index of refraction of air is 1. A ray strikes the prism at angle θ1 and is refracted at angle θ2 . The ray then travels to the other side of the prism and strikes the second surface at angle θ2' and emerges at angle θ1' . The angle between the beam that emerges from the prism and the beam that initially struck the prism is called δ, the angle of deviation. Φ . 2 Since the index of refraction varies with wavelength θ1 and the angle of minimum deviation will be slightly different for each wavelength but θ2 and θ2' will always be the same. δ will be a minimum when θ1' = θ1 . At that point θ2 will equal θ2' and both will equal You can use Snell's Law to find the index of refraction of the prism if you know θ1 and θ2 . is no practical way to measure either angle. However, you can use simple geometry to express θ1 and θ2 in terms of angles that are to measure, namely δmin and Φ. There Φ δ easy θ 1' θ 1 You can show that the index of refraction of a prism as a function of the wavelength, n(λ) , in terms of the apex and the angle of minimum deviation, θ2 θ2' n angle δmin , is Φ⎞ ⎛δ sin ⎜ min + ⎟ 2⎠ ⎝ 2 n(λ)= . ⎛Φ ⎞ sin ⎜ ⎟ ⎝2⎠ δmin can be found experimentally by observing light of known wavelengths through a prism and varying the angle θ1 . This gives you everything you need to calculate n(λ) . This is not a linear function; a plot of n(λ) vs. λ will produce a curve. Equipment spectrometer light shields glass prism (handle with care) lab jack spectrum tube power supply hydrogen tube helium tube table lamp Procedure This experiment has to be done in the dark. Be considerate of other people in the room; be careful about turning your lamp on so that you don't blind others in the room. 1. Set up the spectrometer by placing the slit at 180° and the telescope at 0°. Place one of the spectrum tubes in the power supply, turn it on and set it as close to the slit as possible. View the slit through the telescope. Move the entire spectrometer back and forth until the image of the slit is brightest. 2. If you cannot see the crosshairs in the telescope, move the crosshairs back and forth until they are clear. Slight back lighting helps. 3. A clear image of the slit should appear in the crosshairs. If the image is not clear, adjust the position of the slit and/or the position of the telescope lens. If the image is not at 0° loosen the slit and move it until the image does appear at 0°. Tighten everything. 4. Place the prism in the holder so that a clear side is roughly perpendicular to the beam on the telescope side of the spectrometer and the frosted side is on the right side as you look down on the apparatus. Tighten the screws just enough to hold it in place. Too much pressure will chip the corners of the prism. Raise or lower the holder so that the prism is aligned with the beam. 5. Sight along the edge of the spectrometer until you see the spectrum. Then find the spectrum with the telescope. It may be necessary to adjust the telescope or to move the slit relative to the collimating lens to get the best image. You may also need to raise or lower the prism in its mount. 6. Pick one spectral line and observe it through the telescope as you rotate the prism back and forth in its mount. The line will move back and forth as the prism rotates. Follow it with the telescope. Find the minimum angle of deviation (the smallest angle from 0°) for that wavelength and record λ and δ min . Repeat the procedure for all the lines of hydrogen and helium. The spectrum tubes will got hot; take care when changing them. Do not realign the spectrometer when you change light sources. 7. Turn everything off and disassemble the apparatus. Leave it as you found it. Data Data will consist of the colors of the spectral lines and the angle of minimum deviation for each line. Use 60.0° for the apex angle. Be sure your instructor signs your notebook. Analysis 1. Use the chart in your manual to find the wavelength for each color you found. You may have to do some extrapolation since all the listed colors were probably not visible. 2. Use the apex angle and the angles of minimum deviation to find n(λ) for each wavelength. Fudge a little and calculate n(λ) to four significant digits (three decimal places). 3. Plot n(λ) as a function of λ for the prism. It is important to get a good scale here. If your scale is too coarse or too fine the graph will not be a good display. Put all the results on one graph. Draw the curve that best describes the data. Questions 1. Use a straightedge to make a careful drawing of a prism traversed by a beam of light which emerges at the angle of minimum deviation. Label all the angles necessary for the derivation of n(λ) . 2. Refer to your diagram and derive the equation Φ⎞ ⎛δ sin ⎜ min + ⎟ 2⎠ ⎝ 2 n(λ)= . ⎛Φ ⎞ sin ⎜ ⎟ ⎝2⎠ 3. Look up the index of refraction for different glasses. What kind of glass do you think the prism was made of? 4. If the apex angle of your prism had been significantly lower, say around 15°, how would the data and the results of the experiment have changed? Explain your reasoning. 5. Explain why you could put all your results on one graph. If it applies to you, write "I have not cheated on this lab report" and sign your name. Grading 4 pts Data and Analysis. 3 pts Each for questions 1, ,2, 3, and 5. 4 pts For question 4. Be sure to include sample calculations and make sure your answers have the correct units and proper significant digits. Written answers should be legible, complete and specific. Neatness does count.