Simulated Double-Slit Interference

Introduction

Diffraction and interference are properties of light that are not commonly observed in everyday life. Light we see is composed of different wavelengths, intensities, polarization and phases. A coherent light source, such as laser light, and a diffraction grating, or multiple-slit grating, are typically needed in order to demonstrate interference and diffraction. In this demonstration, double-slit interference patterns are simulated using two coherent, point-source plates.

Concepts

• Interference pattern
• Coherent light
• Wavelength
• Diffraction

Materials

Safety Precautions

Although this activity is considered nonhazardous, please follow normal laboratory safety guidelines.

Procedure

1. Overlap both acrylic plates with concentric circle pattern A so that the circles line up evenly. Place the plates on the overhead projector (see Figure 1).
   {13956_Procedure_Figure_1}
2. Slowly pull the two acrylic plates in opposite directions (one plate to the left and one plate to the right) to show the students the simulated interference pattern that projects on the overhead projector screen. The pattern will resemble the pattern in Figure 2.
   {13956_Procedure_Figure_2}
3. Remove the two acrylic plates from the overhead projector.
4. Obtain the overhead transparency protractor sheet and place it on the overhead projector. Tape the edges of the transparency sheet to secure it to the overhead projector.
5. Line up the center line on one of the acrylic plates with the first dashed line on the second plate. Make sure the acrylic plates are square and the “point sources” are lined up horizontally. The “zero order bright bands” should be perpendicular to the point source separation (see Figure 2). (The “point source” separation is 0.5 cm.)
6. Carefully place the overlapping acrylic plates on top of the protractor overhead transparency so that the midpoint between the point sources lines up with the center of the protractor, the point sources run along the zero line, and the zero order bright bands are bisected by the 90° lines on the protractor sheet (see Figure 3).
   {13956_Procedure_Figure_3}
7. (Optional) Use a ruler to measure the point source separation. Record the actual value on the blackboard (it should be approximately 0.5 cm).
8. Measure the angle that bisects the first bright band (1st order) (see Figure 3). Record this angle on the blackboard. Note: Angles are measured relative to the perpendicular (normal), 90° angle of the zero order bright band. For the example shown in Figure 3, the bisecting angle of the first-order bright band is 30° (90°–60°).
9. If a second-order bright band is present, measure the angle that bisects the second bright band. Record this angle on the blackboard.
10. Repeat step 9 for any higher order bright bands that are observed.
11. Repeat step 5, but line up the center line on one of the acrylic plates with a different dashed line on the second plate.
12. Repeat steps 6–10.
13. After completing the data, use Equation 1 (in the Discussion section) to determine the “wavelength” of the coherent light source.
14. Measure the “wavelength” of the coherent light source to verify the calculated “wavelength.” The wavelength is equal to the distance between the beginning of one dark circle to the beginning of the next dark circle on the concentric circle plate (see Figure 4). (The wavelength is approximately 3.5 mm for Pattern A.)
    {13956_Procedure_Figure_4}
15. Repeat steps 1–14 using the acrylic plates with concentric circle pattern B.
16. What does the interference pattern look when plate A and plate B are used together?

Teacher Tips

• The acrylic plates and overhead projector protractor sheet can be used indefinitely. When stacking the plates for storage, place a sheet of white paper between the plates to prevent scratching the circle patterns.
• Photocopy the Concentric Circle Masters A and B and the Protractor Master onto overhead transparency sheets, enough for six or seven student groups. Pass out to students so that they can follow along with the demonstration.
• The wavelength of the plate point sources and the point source separation are much larger than wavelengths of visible light. However, this is still an excellent simulation of the interference of coherent light because the ratios between the wavelength and point source separation will be the same. Red laser light has a wavelength of approximately 645 nm. The double-slit separation needed for the first order bright band to occur at 15° is approximately 2490 nm. For the simulated interference demonstration, with a point source wavelength of 3.5 mm, the double-slit separation needs to be 13.5 mm for the first order bright band to occur at 15°. The ratio of 645 nm : 2490 nm is the same as the ratio of 3.5 mm : 13.5 mm—equal to 0.26.

Sample Data

Interference Patterns and Calculations

Concentric Circle Pattern A represents a 3.5-mm wavelength point source. A slit separation of 1 cm will produce a pattern similar to Figure 5.

Using Equation 1, the first-order (m = 1) and second-order (m = 2) bright bands will be located at:

1st order: sin θ = (1) × (3.5 mm)/(10 mm)

θ = 20.5°

2nd order: sin θ = (2) × (3.5 mm)/(10 mm)

θ = 44.4°

Concentric Circle Pattern B represents a 5-mm wavelength point source. A slit separation of 2 cm will result in an interference pattern similar to Figure 6. The first- and second-order bright bands will be located at:

1st order: sin θ = (1) × (5 mm)/(20 mm)

θ = 14.5°

2nd order: sin θ = (2) × (5 mm)/(20 mm)

θ = 30°

Discussion

Interference of light occurs when light travels through thin slits that are very close together. The light exiting the thin slit spreads out at a wide angle as if the light originated from the slit as a point source (see Figure 7).

If all the light is the same wavelength and phase, also known as coherent light, then an interference pattern will develop. Laser light is an example of coherent light. An interference pattern develops because the coherent light has to travel different distances to reach the same point. If the path lengths are just right, two light waves will reach the same point “in phase” and result in constructive interference, generating a bright spot of light. Destructive interference occurs when the light waves are “out of phase” as they reach the same point, resulting in the creation of a dark band (see Figure 8). The location of the bright bands obtained when coherent light passes through a diffraction grating can be predicted using Equation 1. Equation 1 relates the angle of the bright bands to the wavelength of the light souce and the slit separation. This equation can also be used for double-slit interference.

λ = wavelength of light
d = slit separation (point source separation)
θ = angle of the bright band from the normal
m = order of the band