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# Wave Optics : Interference

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Two spherical waves with the same amplitude, A, and wavelength, lamda, are spreading out from two point sources S1 and S2 along one side of a barrier. The two waves have the same phase at positions S1 and S2. The two waves are superimposed at a position P. If the two waves interfere constructively at P what is the relationship between the path length difference dx = d2 - d1 and the wavelength. If the two waves interfere destructively at P, what is the relationship between the path length difference and the wavelength.

3. What does it mean to say that two sources of waves are coherent, for instance, the waves in questions 2 above? If the sources in question 2 were two flashlights, would you observe interference at P? Explain.

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This solution contains step-by-step calculations to determine the inference at P and the meaning of coherent waves.

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Please refer to the attachment for the diagram.

Whenever two waves of same wave length superimpose such that the crest of one coincides with the crest of the other (and therefore trough of one coincides with the trough of the other), at point P, constructive interference takes place at point P. The amplitude of the resultant wave is the sum of the amplitudes of the two waves.

As the two wave fronts originating from S1 and S2 are in phase at the starting points, if the difference in the paths of the two waves is an integral multiple of their wave length, the condition ...

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