PHO 101 Photonics Concepts
Three Rivers Community College ONLINE

Home Lab #8

The Diffraction Grating

Materials: laser pointer, diffraction grating slide from OSA kit, clothespins or other supports for components, box or heavy paper for screen, ruler or tape measure with metric (cm) markings

Purpose: In this lab you will use the diffraction grating equation to determine the number of lines per mm on your diffraction grating

Background: The diffraction grating equation describes the angle at which light of a given wavelength is diffracted (bent) after passing through a set of very closely spaced parallel lines. The "lines" may be opaque lines on a transparent background or the grating may be made of "lines" that are simply thicker than the spaces in between.

The diffraction "pattern" that you will see on the viewing screen consists of bright spots ("fringes") where light traveling through different parts of the grating meet and interfere constructively. If the grating lines are held vertically, the row of bright spots will be stretched out in the horizontal direction. The center spot is normally the brightest, and is called the zero order, or m=0 fringe.The spots on either side of the center are numbered the first order fringe (m=1), second order fringe (m=2), and so on. That is, the fringes are "named" by the order number, m.

The location of the fringe of order m is found from the equation:

(Equation 1)

where d is the spacing between the grating lines and the angle q is the angle in the right triangle shown in Figure 1 for the m=2 fringe. (Note that there are two m=2 fringes, one on either side of center.)

The spacing between the slits (d) is calculated by rearranging the above equation to give

(Equation 2)

The fringe order "m" is obtained by counting the fringes from the center of the pattern, and the wavelength l is indicated on the laser. The only remaining challenge is to find the angle q.

Figure 1. The geometry of the diffraction grating lab. Two orders of fringes are shown.

In figure 1, the triangle highlighted in black is a right triangle, so the angle q may be determined using trigonometry. (It would be too difficult to use a protractor!) If the distance to the screen (x) and the distance from the center of the pattern to the "mth" order fringe are known, theta can be found from the right triangle. Remembering the definition of the tangent (tan) function:

(Equation 3)

The value of y is different for each of the "m" fringes. Then,

(Equation 4)

Equation 4 is used to find the angle for each of the "m" fringes measured, and then equation 2 is used to determine the slit separtion "d". Several values of "d" will be averaged to give the final value.

Procedure:

1. Set up the laser pointer and diffraction grating slide so that the light strikes the slide at right angles. Use clothes pins to support the laser and slide. In Figure 2, the grating slide is held between two small boxes and the center order fringe is seen directly in front of the laser pointer. The two first order fringes are very faint, to the either side of the first order. No higher order fringes were seen with this particular grating.

2. Set up a screen about one half meter from the diffraction slide. Be sure the screen is at right angles to the laser beam. You will know that everything is aligned properly if the two first order fringes are the same distance from the center spot.

3. With the laser on, rotate the grating slide an note how the orientation of spots changes. You should see that the m=0 order fringe doesn't move when the grating is rotated.

Measure the distance from the center (m=0) spot to the first two orders (m=1 and m=2) on either side of center- 4 "y" measurements total. If there is no m=2 order, note that in the data table. Some gratings are made to have only the first order- I don't know what kind you have in your kit. Note in the data table how many orders you see.

4. Note the wavelength of the laser printed on the laser warning label. (Turn the laser off first!!) If there is a range of wavelengths (e.g. 650-670 nm) use a wavelength in the center of the range.

5. Calculate the diffraction angles for each of the measured values of "y" using the Equation 4.

6. Using the angles from part 5, and the wavelength of the laser, calculate the line spacing "d" in meters for each measurement from Equation 2.. Calculate the average of all your line spacing measurements.

7. Calculate the number of lines per meter. Since d, the space between lines, is in meters, the number of lines per meter is 1/d. (Usually gratings are specified by number of lines per meter.)

Questions:

1. If you had a blue laser, would the fringes for the orders you measured be closer to the pattern center or further away?

2. Measure the width of your diffraction grating. How many lines make up this grating? (Note that you know how many lines there would be in a meter of the material, so you can determine how many lines there are in the size piece you have.)

 

DATA/OBSERVATIONS/RESULTS

Distance from grating to screen______

Laser Wavelength________________

Number of orders seen (including the center, or m=0)____________

fringe order (m)

distance (y)

angle (q)

line spacing (d)

1

1

2

2

average line spacing =___________________

Something to try:

A CD is like a diffraction grating. Reflect the laser pointer off the surface of a CD (be careful not to direct the light into anyone's eyes!). What do you see? Could you use this experiment to find the groove spacing of a CD? 

© J Donnelly 2001