Introduction:
When light passes through narrow slits, a pattern of bright and dark fringes results. This characteristic behavior of light can only be explained if we think of light as a wave disturbance of some sort. For example, if light simply traveled in straight lines like particles with constant velocity, then one would expect that two bright spots would form when light passes through two narrow slits. Typically however it is possible to see many bright spots, equally spaced.

These many bright spots can be interpreted as the result of interference between two waves, one emanating from each of the slits. The waves have the same wavelength and are in phase at the position of the slits. Each slit illuminates a large area of the screen. The bright spots are produced when the light disturbance arriving from one slit is in phase with the light disturbance from the other slit. In contrast, a dark area results whenever the light from one slit is out of phase with the light from the other slit.

The difference in phase between the two waves occurs because the light from one slit must travel farther (r₂) to the screen than does the light from the other slit (r₁). The amount of this difference is represented by "D" in the upper part of Figure 1. The amount of this phase difference depends on the distance between the slits and the angle from normal at which the light travels.

D = r₂ - r₁            also,   D = d*sin q          (i)

Whenever the difference D equals an integer number of wavelengths, the two light wave disturbances are in phase, so they reinforce each other, and they produce a bright spot on the screen.

D = nl,   n = 0, ±1, ±2, ...                         (ii)

Whenever the difference D correspond to an odd integer number of half wavelengths, the two waves are exactly out of phase, so they cancel each other out, and a dark spot on the screen is the result.

D = nl + l/2,   n = 0, ±1, ±2, ...              (iii)

Alternating bright and dark spots are obtained on the screen as one moves away from the center of the screen (see lower part of Figure 1). The angular position (q_n) of the bright spots can be predicted by combining equations (i) & (ii)

d*sin q_n = nl,            n = 0, ±1, ±2, ...     (iv)

The linear position of the bright spots can be determined by using equation (iv) in combination with a relationship describing the physical configuration of the slits and the screen.

tan q_n = y_n/L,           n = 0, ±1, ±2, ...        (v)

as long as q_n is small, then the following is approximately correct:

tan q_n = sin q_n              and  sin q_n   =  y_n/L

In a similar manner, the linear position of the dark spots can be determined.
 

Purpose:
As indicated by the analysis described above, a clear relationship exists between the spacing of narrow slits and the formation of a pattern of bright and dark spots when light passes through the slits. In this experiment you will determine the spacing between two narrow slits based upon an analysis of the interference pattern that results when you shine light from a laser pointer pen onto the slits. A laser is used because it provides a coherent, monochromatic light source. This means that the light emanating from each slit will be in phase with light from the other slit at the moment that it passes through the slits. Whether the light is in phase at any other position depends on the position, as described above. Monochromatic means that the laser produces light having a single wavelength.
 
 

Materials:
pen pointer laser (3 mW, l = 675nm)       meter stick or ruler
optical bench                                            screen
Cornell interference plate

Investigations: