Young’s Double Slit Experiment

From our discussions of waves you know that waves may interfere with each other creating areas of maximum amplitude and areas of minimum amplitude. Thomas Young discovered that light followed this same pattern

In the early 1800's (1801 to 1805), Thomas Young conducted an experiment. He allowed light to pass through a slit in a barrier so it expanded out in wave fronts from that slit as a light source. That light, in turn, passed through a pair of slits in another barrier (carefully placed the right distance from the original slit). Each slit, in turn, diffracted the light as if they were also individual sources of light. The light impacted an observation screen. Young’s Double Slit Experiment

When a single slit was open, it merely impacted the observation screen with greater intensity at the center and then faded as you moved away from the center. There are two possible results of this experiment: Particle interpretation: If light exists as particles, the intensity of both slits will be the sum of the intensity from the individual slits. Wave interpretation: If light exists as waves, the light waves will have interference under the principle of superposition, creating bands of light (constructive interference) and dark (destructive interference). Young’s Double Slit Experiment

When the experiment was conducted, the light waves did indeed show these interference patterns. The image to the right shows the intensity in terms of position, which matches with the predictions from interference. Young’s Double Slit Experiment

Young's Double Slit Experiment This is a classic example of interference effects in light waves. Two light rays pass through two slits, separated by a distance d and strike a screen a distance, L, from the slits, as in the Figure Double slit diffraction

Impact of Young's Experiment At the time, this seemed to conclusively prove that light traveled in waves, causing a revitalization in Huygen's wave theory of light, which included an invisible medium, ether, through which the waves propagated. Several experiments throughout the 1800s, most notably the famed Michelson-Morley experiment, attempted to detect the ether or its effects directly. They all failed and a century later Einstein's work in the photoelectric effect and relativity resulted in the ether no longer being necessary to explain the behavior of light. Again a particle theory of light took dominance. Young’s Double Slit Experiment

Derivation of Young’s Equations

= Wavelength d = Distance between the slit opening y = Distance between the central fringe and the fringe to be measured n = The number fringe L = The distance between the filter and the screen

The general condition for constructive interference on the screen is simply that the difference in path-length Δ between the two waves must be an integer number of wave-lengths. In other words, where m=0,1,2... Of course, the point P corresponds to the special case where m=0. It follows, from the diagram, that the angular location of the m th bright patch on the screen is given by Likewise, the general condition for destructive interference on the screen is that the difference in path-length between the two waves must be a half-integer number of wave-lengths. In other words, where m=1,2,3... It follows that the angular coordinate of the m th dark patch on the screen is given by

Usually, we expect the wave-length of the incident light to be much less than the perpendicular distance to the screen. Thus, where y measures position on the screen relative to the point. It is clear that the interference pattern on the screen consists of alternating light and dark bands, running parallel to the slits. The distances of the centers of the various light bands from the point are given by where m=0,1,2... Likewise, the distances of the centers of the various dark bands from the point are given by where m=1,2,3... The bands are equally spaced, and of thickness. Note that if the distance from the screen is much larger than the spacing between the two slits then the thickness of the bands on the screen greatly exceeds the wave-length of the light. Thus, given a sufficiently large ratio, it should be possible to observe a banded interference pattern on the screen.