Abstract
The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.
Highlights
In order that the two circular wavefronts intersect each other to trace out the locus of some curve
Substituting (28) and (32) in (27), we arrive at,. This is the analytical equation of the hyperbola representing the locus of all the points of intersection between two circular wavefronts emanating from sources A and B, emitted at times
If the Parallel Ray Approximation (PRA) assumptions are taken into account (i.e. D>>d and d>>λ), the terms in equation (10) can be neglected and it would reduce right back to the classical results (4) and (5) for constructive and destructive interference, respectively
Summary
The double slit experiment was historically the first to decisively demonstrate and establish the wave nature of light, bringing to rest the long-standing debate on whether light had a particle or a wave nature. [1, 2] The apparatus used, consists of two barriers (see Figure 1). The double slit experiment was historically the first to decisively demonstrate and establish the wave nature of light, bringing to rest the long-standing debate on whether light had a particle or a wave nature. Upon arrival at the second barrier, the single circular wave-front is split into two circular wave-fronts by slits S1 and S2. A viewing screen is situated some distance infront of the second barrier. Light from both slits S1 and S2 combine either constructively or destructively at various points on this screen, giving a visible pattern of alternating dark and bright parallel bands, called fringes. Constructive interference gives rise to a bright fringe and destructive interference to a dark fringe (see Figure 2).
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