EXPERIMENT 10 DIFFRACTION AND INTERFERENCE
6-14-2020

OBJECTIVE:
To examine the diffraction pattern formed by laser light passing through a single slit and interference patterns formed by light passing through two slits and to find the wavelength of the laser light.

Enlarged Product Image

EQUIPMENT:
Diffraction Slits Diode Laser (? = 650 nm)

Meter stick Screen

Link to video: https://youtu.be/v09GIce8c2w

PART A: DIFFRACTION FROM A SINGLE SLIT
THEORY:
Diffraction is the bending of all kinds of waves as they pass near an edge or pass through a small opening. The bent, or diffracted, waves then interfere with themselves to create an interference pattern beyond the opening. This ‘diffraction pattern’ looks like that shown in Figure 1. There is a relatively wide and bright central maxima, on both sides of which are the first order minima, m=1, (area of darkness), followed by the first order maxima (bright area). This keeps repeating.

The angle to the minima in the diffraction pattern is given by

(1)

where a is the slit width, ? is the angle from the center of the pattern to the mth minimum, ? is the wavelength of the light, and m is the order (1 for the first minimum, 2 for the second minimum, . . . counting from the center out, as can be seen in the figure).

From trigonometry, we see that:

(2) Figure 1: Diffraction from a single slit

Where L is the distance from the slit to the screen where the diffraction pattern in made. Y is the distance from the center of the pattern to the mth Minima (in Fig. 1 this is shown for m=2). Since the angle ? is usually small, we can use the following approximations, if ? is in radians:

(3)

From equations (2) and (3), we get:

(4)

Hence by equation (1):

(5)

(6)

PROCEDURE:
Watch the video where an introduction to the subject is given, after which the experiment is shown while being performed. The procedure mentioned below is to indicate how the experiment was performed. Stop the video at appropriate locations and take the data from the images.

Link to video: https://youtu.be/v09GIce8c2w

1. Set up the laser at one end of the optics bench and place the Single Slit Disk in its holder about 3 cm in front of the laser. (In the Online Lab, optics bench is not used, but the slit at lase are placed carefully to satisfy the requirement that the laser beam is perpendicular to the plate having the slits).

2. Place a screen at some distance from the slit.

3. Select the 0.04 mm slit by rotating the slit disk until the 0.04 mm slit is centered in the slit holder. Adjust the position of the laser beam from left-to-right and up-and-down until the beam is centered on the slit.

4. Determine and record the distance from the slit to the screen in Table 1.1.

5. Turn off or dim the room lights and mark the positions of the MINIMA in the diffraction pattern on the screen. Measure the distances. In the Online Lab, measure the distances by stopping the video and using the ruler in the image.

6. The distances to measure are between the two first order Dark fringes on either side of the central Maximum, and between the two second order dark fringes (i.e. between m=1 and m= -1, and between m=2 and m= -2). Note that in Fig. 1, the distance Y is between the center and m=2. You will measure the distance from m=2 to m= -2, and then divide by 2 to get Y for m=2. Record them in Table 1.

7. By using the given values of the slit width ‘a’ and the distance to the screen ‘L’, your measured values of ‘Y’, calculate the wavelength of the laser light used. Then find the percent error by using the known value of the wavelength.

8. Repeat with the other silt widths ‘a’.

9. Repeat with a different distance ‘L’.

Note: In some cases, you will see many minima and maxima, while in others you may not see the second minima. In the first case, you can measure distances to higher order (m >2). Use your judgement what value of m to measure based on the available images. Try to use two different orders for each slit width and screen distance. If you want to see the effect of value of ‘m’ on the results, just add more rows to the table.

DATA:
Wavelength of Laser Light = ? = 650 nm