phys1112ch27solutions

phys1112ch27solutions - CHAPTER 27 INTERFERENCE AND THE...

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Unformatted text preview: CHAPTER 27 INTERFERENCE AND THE WAVE NATURE OF LIGHT CONCEPTUAL QUESTIONS ____________________________________________________________________________________________ 1. REASONING AND SOLUTION A radio station broadcasts simultaneously from two transmitting antennas at two different locations. The radio that receives the broadcast could have better reception depending on the location of the receiving antenna. According to the principle of linear superposition, when the electromagnetic waves from the transmitting antenna arrive at the same point, the resultant wave is the sum of the individual waves. The amplitude of the resultant wave depends on the relative phase between the two waves. The relative phase between the waves depends on the path length difference between the two waves. If the two waves arrive at the receiving antenna so that the path length difference between them is equal to an integer number of wavelengths, the two waves will be in phase, they will reinforce each other, and constructive interference will occur. The resulting amplitude of the radio wave will be larger than it would be from either transmitting antenna alone; therefore, the radio reception will be better. If the two waves arrive at the receiving antenna so that the path length difference between them is equal to an odd multiple of half of a wavelength, the two waves will be exactly out of phase, they will mutually cancel, and destructive interference will occur. The receiving antenna will receive little or no signal in this situation. As a result, the radio reception will be very bad. Thus, having two transmitting antennas does not necessarily lead to better reception. ____________________________________________________________________________________________ 2. REASONING AND SOLUTION Constructive interference occurs between waves from two in-phase sources when the difference in travel distances from the sources to the point where the waves combine is the same or equal to an integer number of wavelengths. For a square the distance from any corner to the center is the same. Hence, constructive interference occurs at the center. ____________________________________________________________________________________________ 3. SSM REASONING AND SOLUTION a. The light waves coming from both slits in a Young's double slit experiment have their phases shifted by an amount equivalent to half a wavelength. Since the light from both slits is changed by the same amount, the relative phase difference between the light from the two slits is zero when the light leaves the slits. When the light reaches the screen, the relative phase difference between light waves from the two slits will be the same as if the phase of the waves had not been shifted at the slits. Therefore, the pattern will be exactly the same as that described in the text....
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This note was uploaded on 04/14/2008 for the course PHY 1409 taught by Professor Vasut during the Spring '08 term at Baylor.

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phys1112ch27solutions - CHAPTER 27 INTERFERENCE AND THE...

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