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Interference

INTERFERENCE: TWO SLITS

OBJECTIVE: To study the interference pattern formed by sending light through two parallel slits. To verify that the model used for understanding interference works in predicting the pattern.

THEORY: If light of one color (one wavelength of ) is sent through two parallel slits that are relatively close together, then the light from the slits interferes as it spreads out and overlaps. If the interfered light is projected onto a screen, an interference pattern of bright and dark fringes is seen. The wave theory of light (physical optics) can explain the interference pattern. In fact, it can predict where the bright and dark fringes will appear on the screen. Consider Figure 1 which shows two slits separated by a distance d. The interference pattern from the two slits is observed on a screen that is a distance L from the slits. As long as L is a lot larger than d, then the positions (y)of the centers of the bright and dark fringes on the screen are given by:

(1)

(2)

where y = 0 is at the center of the pattern. Notice that the separation distance (s) of any two consecutive bright fringes or any two consecutive dark fringes is

s =.(3)

This suggests that the bright and dark fringes should have the same width.

If we only consider interference, then theory predicts that all of the bright fringes should be equally bright. However, you will see that the fringe brightness decreases as you move away from the center of the pattern. The reason for this is due to the diffraction of the light (the spreading of the light) coming from both of the slits. We will look at diffraction in a later experiment.

PROCEDURE:

  1. Your instructor will send laser light through two slits (Pair 1) so that the interference fringes are projected onto a distant screen. Your instructor will tell you the wavelength of the source. Record this value of. Also measure the distance L from the slits to the screen.
  1. Observe the interference fringes. Observe and note if the bright fringes and dark fringes have equal widths. Observe and note if the bright fringes are all equally bright.
  1. Measure the separation distance s between the centers of two consecutive dark fringes.
  1. Now your instructor will send the light through two slits (Pair 2) that are closer together. Observe what happens to the fringe pattern. Again measurethe separation distance s.
  1. Now your instructor will replace the laser with a laser of a different wavelength. Record the new wavelength.
  1. Your instructor will send the new laser light through the original slits (Pair 1). Again measurethe separation distance s between two dark fringes.
  1. Now the light will be sent through the Pair 2 slits.Again measurethe separation distance s between two dark fringes.

REPORT:

  1. Do the dark and bright fringes from double slit interference have equal widths as predicted? Do the bright fringes have equal brightness? If not, describe the variation in brightness.
  1. What happens to the separation of the fringes as the two slits get closer together? Is this consistent with the wave theory of light that models interference?
  1. What happens to the fringe separation as the wavelength of the light is reduced? Is this expected?
  1. Use Eq. (3) to calculate the distance between the slits (d) for Pair 1. Calculate two values for d, one for each of the laser wavelengths. Express the distances in millimeters. Remember that:

1 mm (millimeter) = 1x10-3 m 1m (micron) = 1x10-6 m 1 nm = 1x10-9 m

Ideally, the two values should be equal. Are your values close to each other? What could cause a discrepancy?

  1. Repeat the calculations of d for Pair 2. Again comment on the agreement of the two values.