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MSU PHY 252 - Lab Practical 2

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PHY 252 Fall 2010 Practical Lab 2 The Diffraction Grating OBJECTIVES: 1) Observe the interference pattern produced when laser light passes through multiple-slit grating (a diffraction grating). 2) Graphically verify the wavelength of the laser light using the data collected from the interference pattern produced when the light passes through a diffraction grating. CAUTION! The laser is a device that can produce an intense, narrow beam of light at one wavelength. NEVER look directly into the laser beam or its reflection from a mirror, etc. INTRODUCTION Interference occurs when two or more coherent waves overlap. (Coherent means that the waves have a fixed phase relationship.) Constructive interference takes place at certain locations where two waves are in phase (for example, both waves have maximum). Destructive interference takes place where two waves are out of phase (for example, one wave has maximum, the other has minimum). The simplest interference patterns involve plane waves (collimated or parallel light beams). In this experiment, we will use a laser as our light source. A laser produces collimated and coherent light beams at one wavelength.Multiple-slit interference (a diffraction grating) Figure 1: Intensity distribution of a diffraction grating Although a multi-slit grating is commonly referred to as a diffraction grating, a more appropriate name for it is an interference grating. The phenomenon that is observed is interference and not as its name suggests diffraction. The condition here for interference maximum is the same as for double-slits, but the pattern may be very different because d (the slit spacing) for gratings is very small. d sin θm = mλ or sinmdλθ= (1) If a graph of sinmθvs. mis constructed, it has the form of a straight line with mplaying the role of x and sinmθplaying the role of y. The line should have an intercept of zero and a slope of dλ. Note: 1d is the ruling density which will be given in lines/mm. Using the slope of the line and the ruling density, the wavelength of the laser light can be calculated.The angles involved when using the diffraction grating are large; therefore you cannot use the small angle approximation here. In Figure 1 above, sinθ (for m = 3) is expressed as the ratio of the opposite side of the right triangle (3x) to the hypotenuse of the right triangle ()223Dx+. The distances xm are measured from the location of the central maximum, x0. Equation 1 can be expressed as: 22xmdDxλ=+ (2) The distances xm are positive for positive values of m and are negative for negative values of m. The order of the maxima can take on the values of m=0, ±1, ±2, … PROCEDURE The wavelength (λ) of the green diode laser used in this experiment is ( )4532 10 5.32 .10 10nm mm−±=±×. The screen to diffraction grating distance D and the ruling density 1d you will use will be given to your answer sheet of the practical lab. 1. Place the grating in the laser beam at the distance D specified on your answer sheet in front of the screen and record this distance in your Excel spreadsheet. 2. Record the labeled ruling density (grooves/mm) in your Excel spreadsheet. 3. Tape a piece of paper across the screen. Mark carefully the positions of the principal maximum and the interference maxima. You should mark and record the location of the central maximum, both first order maxima and both second order maxima. Remove the paper from the screen and attach it to your lab report. 4. Measure the distance of each interference maximum from the principal maximum (xm) and record them in your Excel spreadsheet. Have Excel calculate ()22mDx+ and22sinmmxDxθ=+ for each of the maxima. 5. Transfer your data table into Kaleidagraph and make a plot of sinmθvs. m. Fit your plot with a best-fit line and have Kaleidagraph display the equation of the line along with the uncertainties in the slope and intercept. QUESTIONS 1. Sketch the pattern you observed when the laser light passed through a diffraction grating (i.e. attach the piece of paper from your screen). Label each of the interference maxima. 2. What is the slope of your graph?3. From the slope of your graph and the ruling density, calculate the wavelength of the laser light and its uncertainty (show calculations). 11slopedslopedδδδλ λ⎛⎞⎛⎞⎜⎟⎜⎟⎝⎠⎜⎟=+⎛⎞⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠ 4. Discuss the consistency of your measured value of the wavelength from question 3 with the accepted value of 532 10 nm±. 5. If the grating density, 1dwere halved what would be the highest possible order of the resulting interference maxima? Comparing Data It is often necessary to compare two different pieces of data or results of two different calculations and determine if they are compatible (or consistent). In just about every experiment in this course you will be asked if two quantities are compatible or consistent. The following describes how to determine if two pieces of data are consistent (or compatible). Use this procedure to answer the question at the end and use it as a reference whenever you are asked if two pieces of data are compatible or consistent. Let’s denote the pieces of data by d1 and d2. If d1 = d2 or d1 - d2 = 0, clearly they are compatible. We often use Δ (pronounced “Delta”) to denote the difference between two quantities: Δ = d1 – d2 (8) This comparison must take into account the uncertainties in the observation of both measurements. The data values are d1 ± δd1 and d2 ± δd2. To perform the comparison, we need to find δΔ. The addition/subtraction rule for uncertainties is: δΔ = δd1 + δ d2 (9) Our comparison becomes, “is zero within the uncertainty of the difference Δ?” This is the same thing as asking if: ⏐Δ⏐ ≤ δΔ (10) Equation (9) and (10) express in algebra the statement “d1 and d2 are compatible if their error bars touch or overlap.” The combined length of the error bars is given by (9). ⏐Δ⏐ is the separation of d1 and d2. The error bars will overlap if d1 and d2 are separated by less than the


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