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# Can the sum of the magnitudes of two vectors ever be equal ISBN: 9780470469088 189

## Solution for problem 1 Chapter 3

Fundamentals of Physics Extended | 9th Edition

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Problem 1

Can the sum of the magnitudes of two vectors ever be equal to the magnitude of the sum of the same two vectors? If no, why not? If yes, when?

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Chapter 28: Physical Optics­ Interference and Diffraction  If two waves occupy the same space, their amplitudes add at each point. They may interfere either constructively or destructively  Conditions for dark fringes (destructive interference) in a two­slit experiment: dsinα = m− 1 λm=1,2,3,… o Above central bright fringe: ( ) 2 1 o Below central bright fringe: inα = ( ) 2 λm=−1,−2,−3,…  Interference is only noticeable if the light sources are monochromatic (so all the light has the same wavelength) and coherent (different sources maintain the same phase relationship over space and time)  Interference will be constructive

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##### ISBN: 9780470469088

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Can the sum of the magnitudes of two vectors ever be equal