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Solved: Phasor Diagram for Eight Slits. An interference
Chapter 36, Problem 61P(choose chapter or problem)
Phasor Diagram for Eight Slits. An interference pattern is produced by eight equally spaced, narrow slits. Figure 36.14 shows phasor diagrams for the cases in which the phase difference \(\phi\) between light from adjacent slits is \(\phi=\pi\), \(\phi=\pi / 4\), and \(\phi=\pi / 2\). Each of these cases gives an intensity minimum. The caption for Fig. 36.14 also claims that minima occur for \(\phi=3 \pi / 4\), \(\phi=5 \pi / 4\), \(\phi=3 \pi / 2\), and \(\phi=7 \pi / 4\). (a) Draw the phasor diagram for each of these four cases, and explain why each diagram proves that there is in fact a minimum. (Note: You may find it helpful to use a different colored pencil for each slit!) (b) For each of the four cases \(\phi=3 \pi / 4\), \(\phi=5 \pi / 4\), \(\phi=3 \pi / 2\), and \(\phi=7 \pi / 4\), for which pairs of slits is there totally destructive interference?
Equation Transcription:
π
π
π
π
π
π
π
π
π
π
π
π
Text Transcription:
phi
phi=pi
phi=pi/4
phi=pi/2
phi=3pi/4
phi=5pi/4
phi=3pi2
phi=7pi/4
phi=3pi/4
phi=5pi/4
phi=3pi2
phi=7pi/4
Questions & Answers
QUESTION:
Phasor Diagram for Eight Slits. An interference pattern is produced by eight equally spaced, narrow slits. Figure 36.14 shows phasor diagrams for the cases in which the phase difference \(\phi\) between light from adjacent slits is \(\phi=\pi\), \(\phi=\pi / 4\), and \(\phi=\pi / 2\). Each of these cases gives an intensity minimum. The caption for Fig. 36.14 also claims that minima occur for \(\phi=3 \pi / 4\), \(\phi=5 \pi / 4\), \(\phi=3 \pi / 2\), and \(\phi=7 \pi / 4\). (a) Draw the phasor diagram for each of these four cases, and explain why each diagram proves that there is in fact a minimum. (Note: You may find it helpful to use a different colored pencil for each slit!) (b) For each of the four cases \(\phi=3 \pi / 4\), \(\phi=5 \pi / 4\), \(\phi=3 \pi / 2\), and \(\phi=7 \pi / 4\), for which pairs of slits is there totally destructive interference?
Equation Transcription:
π
π
π
π
π
π
π
π
π
π
π
π
Text Transcription:
phi
phi=pi
phi=pi/4
phi=pi/2
phi=3pi/4
phi=5pi/4
phi=3pi2
phi=7pi/4
phi=3pi/4
phi=5pi/4
phi=3pi2
phi=7pi/4
ANSWER:
Β When their phasors are in opposite directions Β then is totally destructive interference between two slits.
Β totally destructive interference occurs between slits four apart.
Β For Β totally destructive interference occurs with every second slit.
Β (a) For eight slits, the phasor diagrams must have eight vectors. The diagrams for each specified value of Ο are sketched In each case the phasors all sum to zero.
