### Wave Interference and Phase DifferenceIn the study of wave mechanics, understanding the concept of interference is crucial. This section explores the phenomenon of constructive interference through a practical problem involving coherent light waves.**Problem Statement:**Two beams of coherent light travel through different paths, arriving simultaneously at point P. To achieve maximum constructive interference at point P, what should the phase difference between these two waves be?**Options:**1. The phase difference between the two waves is \(2\pi\).2. The phase difference between the two waves is \(\frac{5\pi}{2}\).3. The phase difference between the two waves is \(\frac{\pi}{2}\).4. The phase difference between the two waves is \(\pi\).5. The phase difference between the two waves is \(\frac{\pi}{4}\).**Key Concept:**For maximum constructive interference to occur, the phase difference between two waves should be an integer multiple of \(2\pi\). This ensures that the crests and troughs of the two waves align perfectly, thus amplifying the resultant wave's amplitude.**Explanation:**- **Phase Difference \(2\pi\):** This corresponds to a complete cycle where one wave has traveled one full wavelength more than the other. Since \(2\pi\) is an integer multiple of \(2\pi\), this creates constructive interference.- **Phase Difference \(\frac{5\pi}{2}\) and \(\frac{\pi}{2}\):** These values are not integer multiples of \(2\pi\), and hence do not align the waves for maximum constructive interference.- **Phase Difference \(\pi\):** This represents a half-wavelength difference, leading to destructive interference rather than constructive interference.- **Phase Difference \(\frac{\pi}{4}\):** Again, this is not an integer multiple of \(2\pi\), and thus would not result in constructive interference.**Correct Answer:**- The phase difference between the two waves is \(2\pi\).Understanding these principles is fundamental in optics and wave theory, especially in applications such as interferometry, diffraction, and the analysis of coherence in light waves.

Introduction: The coherent waves are that type of wave which have frequency and amplitude same, and…

Two beams of coherent light travel different paths arriving at point P. If the maximum constructive interference is to occur at point P, what should be the phase difference between the two waves? O The phase difference between the two waves is 2n. O The phase difference between the two waves is 5n/2. O The phase difference between the two waves is n/2. O The phase difference between the two waves is n. O The phase difference between the two waves is n/4.

Two beams of coherent light travel different paths arriving at point P. If the maximum constructive interference is to occur at point P, what should be the phase difference between the two waves? O The phase difference between the two waves is 2n. O The phase difference between the two waves is 5n/2. O The phase difference between the two waves is n/2. O The phase difference between the two waves is n. O The phase difference between the two waves is n/4.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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ASAP
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