The Index of Refraction of Air 4.pdf

The Index of Refraction of Air PHYS 463 LAB Purpose: Find the index of refraction of air using Michelson interferometer. Theory: In this experiment you will measure the index of refraction of air by comparing the optical path lengths of two columns of air of equal physical length but at...

The Index of Refraction of Air PHYS 463 LAB Purpose: Find the index of refraction of air using Michelson interferometer. Theory: In this experiment you will measure the index of refraction of air by comparing the optical path lengths of two columns of air of equal physical length but at different pressures. The Instrument used to compare optical path lengths is the Michelson Interferometer. In an interferometer (Figure 1) a light beam (in this case a helium-neon laser) is incident on a partially silvered glass plate (GP) placed 45º with respect to the beam. The beam is split, part of it traveling to mirror M1 at the end of the side arm. This beam is reflected by M1, returning through GP to strike the screen. The other part of the original beam goes through the glass plate Figure 1. The Michelson Interferometer. and the cell to mirror M2. It is reflected by M2 through the cell to the glass plate where it is reflected to the screen. The two beams arriving at the screen produce an interference pattern.  An interference pattern is normally a series of bright and dark concentric circles (Figure 2), because of the imperfections in the mirrors of our interferometers, the circles may be distorted. Figure 2. Ideal interference pattern. In the bright regions of the pattern, the crests of the waves of the two beams arrive together. In the dark areas the crest of one wave arrives at the same time as the trough of the other. If the optical path length of one beam changes by one wavelength, the interference pattern is shifted by one fringe. The optical path length is equal to : 𝑛𝐿 where n is the Index of refraction and L is the physical path length. The optical path length can be varied by changing either n or L. L The opticalpathcanbevarieby Chaffins In our experiment the one beam passes through the cell of length L. Because the beam passes through the cell twice, the optical path length is : 2𝑛𝐿 The air will be removed from this cell, changing the refractive index, n. The other beam passes through the same length of air, but with no cell in that beam, the pressure will remain constant. If the refractive index changes by ∆n, the path length changes by: 2∆𝑛𝐿 As the air is removed, the pattern will shift by one fringe at each time the refraction index changes by an amount : ∆𝑛 = 𝜆/2𝐿 A shift of m fringes will occur when the refractive index changes by an amount : ∆𝑛 = 𝑚𝜆/2𝐿 The refractive index for most gases is close to 1. For air and other ideal gases, the difference between the refractive index and 1 is proportional to the pressure of the gas. Thus we define the refractive index of air : 𝑛 = 1 + 𝑘𝑝 where p is the air pressure and k is an unknown constant. When the pressure is changed, the change in the refraction index is : ∆𝑛 = 𝑘∆𝑝 We can therefore relate the number of fringes shifted, m, to the change in pressure : ∆𝑛 ∆𝑝 = = 𝑚𝜆/2𝐿𝑘 𝑘 Therefore the unknown constant, k, is given by : 𝑘 = 𝑚𝜆/2𝐿∆𝑝 Thus if you measure m fringes while the pressure changes by an amount ∆p, you can calculate the refraction index of air at room temperature using : 𝑛 = 1 + 𝑚𝜆𝑝/2𝐿∆𝑝 (1) Experiment : Warning: The Interferometer glass plate and mirrors have very sensitive surfaces. Please do not touch the mirror or the plates. Call your Instructor before making any adjustments that require you to touch any of the glass surfaces. Apparatus: Michelson interferometer - He-Ne laser – Cell – Exhaust fan with the indicator to measure the air pressure upon discharge Procedure: 1. peace be tube pump air slot higher discharge cell and the other end of the tube arrive air intake slot in the pump 2. Be sure to close all outlets the pump 3. Start gradually withdraw air from the a gradual discharge pressure cell on the arm pump keep drawing until you pray for maximum the pump discharge 4. Invited the air gradually returns in the cell until the equivalent atmospheric pressure during the 5. Record pressure of the pump and the index record m 6. Pull the air now to a lesser extent from step 3 7. Repeat 8 times until reaching the lowest value dump you can access them 8. Draw a relationship between( m) the Y and ( p) the X 9. Record fringe to the atmospheric pressure of the graphic mat 76 cm hg 10. calculate value of the refractive index 11. calculate the ratio of error in reading Results : Pressure (cm\hg) Fringes ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ………………….