Double Slit Interference

Figure 1

When the angles to the fringes are small, then it can be assumed that:

By using trigonometry, it can be shown that:

where y is the distance between the mth bright fringe and the central maximum, and D is the distance from the slits to the screen center point. By using the three previous equations, the following formula can be achieved:

The spreading of light after passing through an aperture is known as diffraction. In addition to the interference caused by the superposition of the laser beams coming from two slit, a diffraction happens at each of the two slits which results in the envelope shown in the next page.

Figure 2

Procedure and Observations:

Required Apparatus:

1. Track and Screen from the Basic Optics System
2. Diode Laser
3. Multiple Slit Disk
4. White Paper        
5. Meter Stick

Figure 3: The experimental setup

First the optical bench was set up with the laser on one end of the optics bench and the white screen on the other end. Then the multiple slit set (in its mount) was placed on the optical bench approximately 3 cm in front of the laser source. Then the laser was turned on, and the room light was turned off. The multiple slit disk was rotated until laser light shined through the double slit set which had separation (d) of 0.25 mm, and width (a) of 0.04 mm. A sheet of white paper was hold in front of the laser light on the screen, and the positions of central maximum and first two bright fringes on one side of it were marked on the paper. Then the paper was removed and the distances between the central maximum and the other maximums were measured with meter stick. Also the distance between the screen and the slit disk was measured and recorded. After that, the slit disk was rotated to a new double slit with 0.04 mm width and 0.50 mm slit separation, and the same procedure was repeated. For the third time the slit disk was moved to another new double slit with 0.08 mm with and 0.25 mm slit separation, and again the same procedure was repeated. The wavelength was the same through the whole experiment ( = 650 nm). Finally all the data obtained from the experiment were recorded in three tables.

Table 1: Data for the 0.04 mm / 0.25 mm Double Slit

Table 2: Data for the 0.04 mm / 0.50 mm Double Slit

Table 3: Data for the 0.08 mm / 0.25 mm Double Slit

Calculations, Graphs and Results:

For each of three different double slits, the following formula was used to calculate the slit separation for both first and second order:

Then, the percentage difference was computed for each case using the calculated slit separation and the one written on the multiple slit disk.

1) 0.04 mm width, 0.25 mm slit separation

a) For First order (m=1):  

b) For Second order (m=2):

Table 4 (0.04 mm / 0.25 mm Double Slit)

2) 0.04 mm width, 0.50 mm slit separation

a) For First order (m=1):  

b) For Second order (m=2):

Table 5 (0.04 mm / 0.50 mm Double Slit)

3) 0.08 mm width, 0.25 mm slit separation

a) For First order (m=1):  

b) For Second order (m=2):

Table 6 (0.08 mm / 0.25 mm Double Slit)

Discussion of Results And Conclusions:

        It was observed in this experiment that the distance between a bright fringe and the central maximum in the interference pattern has the same value that is given by theory. In this experiment slit separation was calculated based on the wavelength of the laser, distance from the slits to the screen, and distance from centre of the pattern to side bright fringes. Two important facts were observed in the experiment. First, increase in the slit separation resulted in increase in the distance between bright fringes. Second, increase or decrease in the slit width had no effect on the distance between bright fringes. The value obtained for slit separation in each of three different cases was close to the actual slit separation which was written on the multiple slit disk. The calculated values for slit separation had a deviation percent of 8%, which is relatively a good result, but it could be improved by eliminating sources of error. There were several sources of error in this experiment. One source of error lies in using the meter stick for measuring the distance from the slits to the screen, and the distance from the central maximum to the side bright fringes, which involves reading error. The error in measuring the distance between bright fringes could be reduced by using an electronic device which could help in measuring the precise value of distance between maximums. Preventing the screen from moving could also contribute to reducing the error. Another source of error could be the screen not being parallel with the multiple slit disk.

      The value of the slit separation that was calculated in this experiment was close to the written value on the disk. Finding a lower value for d shows that in reality other factors (sources of error); mentioned above, have to be taken into account. In addition, another source of error could be minimized by measuring the distance from the center of the pattern to the maxima of order 10 and then dividing it by ten.

References:

1. PCS 125 Lab Manual (2008 fall), Department of Physics, Ryerson University, Toronto.
2. http://en.wikipedia.org/wiki/Double-slit_experiment