![]() L is the slit-barrier-screen distance, O(0, 0) is the origin, M(0, L) is the center of the screen, P( x, L) is an arbitrary point on the screen where light rays S 1 P and S 2 P meet, S 1 S 2 = d is the inter-slit distance, and are the slit source positions. ![]() In the coordinate reference system chosen, the origin O lies midway between the slit sources and the positive axes directions are as indicated in the figure inset.įigure 3. The standard formula for path difference ( δ) that can be found in many physics textbooks is δ = r 1 − r 2 = d sin θ, where d is the inter-slit distance, r 1 and r 2 are the distances of the arbitrary point P on the screen from slits S 1 and S 2, respectively and θ is the angle as shown in figure 3. The formation of a bright or dark fringe depends on whether the interference is either constructive or destructive in nature, which in turn depends on the difference in the lengths of the paths taken by light rays from S 1 and S 2 to reach the particular point P on the screen (see figure 2). The two slits act as coherent sources emanating circular ripples of light that interfere with each other to produce a pattern of alternating bright and dark bands called fringes on the distant screen (see figure 1). In its bare essence, the apparatus consists of a barrier with two very narrow slits S 1 and S 2, and a screen placed at a suitable distance from the slit barrier. It helped bring to rest the then long-standing debate on whether light had a particle or a wave nature. The double slit experiment was historically the first to decisively demonstrate and establish the wave nature of light. In addition, a pair of equivalent laws of proportionality are predicted that govern the distribution of fringes independent of the shape of the detection screen employed. This paper further builds on that work by laying down the mathematical framework necessary for counting fringes and then comparing their distributions on differently shaped screens, using MATLAB software package for numerical–graphical simulation. In the new analysis however, all such approximations were discarded and a hyperbola theorem was forwarded which was then suitably applied to determine the exact fringe positions on screens of varied shapes (linear, semi-circular, semi-elliptical). ![]() This was owing to the adoption of some needless and paradoxical assumptions to help simplify the geometry of the slit barrier-screen arrangement. In prior work by the same author, it was shown that the conventional analysis of Young's experiment that is used in many introductory physics textbooks, suffers from a number of limitations in regards to its ability to accurately predict the positions of these fringes on the distant screen. ![]() A screen placed on the other side captures a pattern of alternating bright and dark bands called fringes which are formed as a result of the phenomenon of interference. In the experiment, light is made to pass through two very narrow slits spaced closely apart. It was expounded by the English physician-physicist Thomas Young in 1801 and it soon helped lay to rest the then raging Newton–Huygens debate on whether light consisted of a fast-moving stream of particles or a train of progressive waves in the ether medium. The double slit experiment was the first demonstrative proof of the wave nature of light.
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