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Unformatted text preview: The Principle of Linear Superposition 1 Conditions for Interference When two or more light waves meet at a given point, their electric fields combine ( interfere ) according to the laws of linear superposition: The waves can add together either constructively or destructively. In constructive interference , the amplitude of the resultant wave is greater than that of the individual waves. In destructive interference , the amplitude of the resultant wave is less than that of the individual waves. Interference effects between two or more light sources are observable, 1. if the sources are coherent , ie they must maintain a constant phase with respect to each other, and 2. if the sources produce light of identical wavelengths. If a single wavelength source is used to illuminate a screen with two small slits, the light emerging from the two slits is coherent. Dr.D.Wackeroth Spring 2005 PHY102A The Principle of Linear Superposition 2 Youngs Double-Slit Experiment Interference in light waves from two sources was first demonstrated in 1801 by Thomas Young: The light from the two slits produces on a screen a visible pattern of a series of bright and dark parallel bands called fringes . The bright (dark) bands are due to constructive (destructive) interfer- ence. Dr.D.Wackeroth Spring 2005 PHY102A The Principle of Linear Superposition Quantitative description: A wave from the lower slit travels farther than a wave from the upper slit by an amount l = d sin , where d is the separation of the two slits. This equation assumes that the distance of the screen to the slits, L , is L d . Dr.D.Wackeroth Spring 2005 PHY102A The Principle of Linear Superposition Constructive interference occurs, if the path difference is an integral multiple of the wavelength: l = d sin = m (1) with m = 0 , 1 , 2 ,... . m is called the order number of the fringe. The central fringe is called the zeroth-order maximum ....
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