Lab Diffraction

College Physics Lab
Diffraction Return to Lab Main

Introduction:

When light passes through a narrow slit, a pattern of bright and dark fringes results. This characteristic behavior of light can only be explained if we think of light as a wave disturbance of some sort. For example, if light simply traveled in straight lines like particles with constant velocity, then one would expect that a single bright spot in the shape of the slit would form when light passes through a narrow slit. Typically however it is possible to see many bright spots, spaced at regular intervals.

These many bright and dark spots can be interpreted as the result of interference of light emanating from different parts of the slit. Mathematical analysis of the situation yields the following inferences. At the center of the illumination pattern is a bright spot. This corresponds to the condition that light from all parts of the slit travels the same distance to the screen so that all light is in phase and constructive interference results. Dark spots in the illumination pattern are predicted by a simple formula.

w*sin qm = ml, m = ±1, ±2, ...

In this formula w represents the slit width, q_m is an angle representing the direction in which the light is traveling, l represents the wavelength of the light, and m represents the order of the dark spot. The quantity w*sinq_m represents the path length difference between light leaving one edge of the slit and light leaving the other edge of the slit. When that path length difference equals an integral number of wavelengths, the total light arriving at a point on the screen destructively interferes. This results in a dark spot. In between the dark spots the light varies in intensity. The point between dark spots where the intensity is greatest is at a position roughly halfway between the dark spots but there is no simple relationship which predicts this position.

The linear position of the dark spots (y_m) on the screen can be determined by using the equation above in combination with a relationship describing the physical configuration of the slit and the screen which is a distance L away from the slit.

tan q_m = y_m/L, m = ±1, ±2, ...

as long as q_m is small, then approximately

tan q_m = sin q_m and sin q_m = y_m/L

This relationship assumes that the center bright spot is located at position y = 0.

According to Babinet's principle, a diffraction pattern will result when waves are incident on an obstruction. The pattern that results from diffraction by a narrow solid object is the same as the pattern that results from diffraction by a narrow slit having the same dimensions as the obstruction. The location of the dark spots follows the above relationships where w is the width of the obstruction.

Purpose:
As indicated by the analysis described above, a relationship exists between the width of the slit and the formation of a pattern of bright and dark spots when light passes through the slit. In this experiment you will explore the applicability of this relationship. In the first activity you will use this relationship to determine the width of a narrow slit. In the second activity you will use the relationship to determine the size of a small object, such as a hair.

In these activities you will use a laser pen pointer to produce the diffraction pattern. The laser provides a coherent monochromatic light source. Monochromatic means that the laser emits light having a single wavelength.

Materials:
pen pointer laser (3 mW, l = 675 nm)            meter stick or ruler
optical bench                                                  screen
Cornell Interference Plate                                hair

Safety Tip!
Be careful in how you direct the laser!
Intense viewing of the beam can't do you any good!

Activities:
I. Diffraction by a single slit.
Procedure:

1. On an optical bench set up a white screen with printed at one end. Set up the interference plate at a position towards the other end. Close to the plate make an arrangement to hold the laser in place. Direct the laser so that it covers the single slit which is directly above the double slit used in the previous lab. This is the second narrowest slit.

2. Observe the diffraction pattern that results. Adjust the positions of the plate and the laser so that the diffraction pattern on the screen is convenient to measure. Are all of the bright spots the same brightness? Is there a pattern in the way their brightness changes? Describe.

3. Identify the central bright spot and measure its position, y₀.

4. Measure the position, ym,on the screen of several orders of dark spots on either side of center. Record this information together with the order of the fringe "m." The first dark spot next to the center may not look completely dark, but you can infer its position by identifying the spacing to the next dark fringe (adjacent dark spots on either side of center are equally spaced). Consider the dark spots on one side of center to be "positive" and the fringes on the other side to be "negative." Note qualitatively the relative brightness of each measured fringe.

5. Construct a predicted relationship between the quantities y_m and m.

6. Plan a graph of your data that should result in a straight line. Does your graph actually exhibit a straight line? Analyze the graph to determine an estimate of the width of the slit.
Compare your result to the known value of 0.0044 cm.

7. Adjust the glass plate so that the laser illuminates the double slit directly across the plate from the single slit you have been using. Note any missing orders relative to the center of the pattern. How does the distance to the missing orders compare to the positions of the dark spots of the single slit diffraction pattern?

II. Diffraction by a human hair.
Procedure: 1. On an optical bench set up a white screen with printed scale at one end. Ask your lab partner to sacrifice a hair for science. With a little tape fasten the hair across the opening of the laser so that the hair is illuminated when the laser is turned on. Place the laser in its holder on the optical bench and orient it so that its light projects onto the screen and the diffraction pattern is projected along the length of the scale.

2. Observe the interference pattern that results. Adjust the positions of the screen and the laser so that the interference pattern on the screen is convenient to measure. Do all of the bright spots have the same brightness? Is there a pattern in the way their brightness changes? Describe.

3. Identify the central bright spot and measure its position, y₀.

4. Measure the position, y_m,on the screen of several orders of dark spots on either side of center. Record this information together with the order of the fringe "m." The first dark spot next to the center may not look completely dark, but you can infer its position by identifying the spacing to the next dark fringe (adjacent dark spots on either side of center are equally spaced). Consider the dark spots on one side of center to be "positive" and the fringes on the other side to be "negative." Note qualitatively the relative brightness of each measured fringe.

5. Construct a predicted relationship between the quantities y_m and m.

6. Plan a graph of your data that should result in a straight line. Does your graph actually exhibit a straight line? From your graph determine the best value for the width of your hair.

7. From your graph determine the highest and lowest reasonable values for this quantity.