Physics 2 Lab DIFFRACTION AND INTERFERENCE

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.

EQUIPMENT:

Diffraction Slits Diode Laser (λ = 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, θ is the angle from the center of the pattern to the mth minimum, λ 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 θ is usually small, we can use the following approximations, if θ 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 = λ = 650 nm

Distance to Screen L	Width of slit a	Order m	Distance between side orders 2Y	Distance from center to order Y	Calculated value of wavelength (eqn. 6)	Percent error in λ
80.2 cm	0.16 mm
	0.08 mm
	0.04 mm
	0.02 mm
536 cm	0.16 mm
	0.08 mm
	0.04 mm
	0.02 mm

Average wavelength found by experiment = ___________

Percent error in the average wavelength = ___________

PART B: INTERFERENCE FROM DOUBLE SLITS

THEORY:

When light passes through two slits, the two light rays emerging from the slits diffract, and the diffracted rays interfere with each other and produce interference fringes. The angle to the maxima (bright fringes) in the interference pattern is given by

(7)

where d is the slit separation, θ is the angle from the center of the pattern to the mth maximum, λ is the wavelength of the light, and m is the order of the MAXIMA (0 for the central maximum, 1 for the first side maximum, 2 for the second side maximum, . . . counting from the center out). See Figure 2.

From trigonometry, we see that:

(2)

Where L is the distance from the slit to the screen where the interference pattern in made, and Y is the distance from the center of the interference pattern to the mth Maxima. Since the angle θ is usually small, we can again use the approximations, for θ in radians:

(3)

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

(4)

Hence by equation (7):

(8)

(m = 0, 1, 2, 3, …) (9)

While the interference fringes are created by the interference of the light coming from the two slits, there is also a diffraction effect occurring at each slit due to Single Slit Diffraction. This causes the Diffraction envelope as seen in Figure 3. The interference patterns are seen inside the diffraction envelope. We do not see any interference fringe where the diffraction envelope is a minimum.

Figure 2: Interference due to Double Slit Figure 3: Interference inside Diffraction Envelope

PROCEDURE:

Same as for Part A (Diffraction from a Single Slit), except that now the distance between the MAXIMA on either side of the central maximum are noted. These distances are much smaller than the distances for the Diffraction Minima, and therefore measurable only when the screen is at the far distance from the slits.

Point to remember: for Diffraction from single slit, we measure distances between the dark fringes, and position of fringe m = 1 is in the center of the first dark patch outside the central maximum. For Interference with double slit, we measure the distances between the centers of the bright fringes. The position of fringe m = 1 is the center of the first bright fringe next to the central one.

As before, use your judgement to select two values of ‘m’ for which ‘Y’ is measured.

If you wish to take more data, just add more rows to the table.

In your report, discuss the effect of slit width on the fringes.

DATA

Wavelength of Laser Light = λ = 650 nm

Distance from Slits to Screen = L = 536 cm

Distance between slits d	Width of slits a	Order m	Distance between side orders 2Y	Distance from center to order Y	Calculated value of wavelength (eqn. 9)	Percent error in λ
0.50 mm	0.08 mm
0.25 mm	0.08 mm
0.50 mm	0.04 mm
0.25 mm	0.04 mm

Average wavelength found by experiment = ___________

Percent error in the average wavelength = ___________