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Lecture 11: Interference
February 27, 2025
Reading Assignment
- Read: 14.6, 32.1-32.2; Supplementary Reading Ch 1.3
- Study: Exs 14.5; Supp Exs 1-3, 1-4
Objectives
- (Continuing objective) Describe applications of the concepts of induction, waves, and light to everyday “real life” situations.
- For interference problems, determine the relative phase difference from path length differences, and use the method of phasors to determine the total amplitude and the relative intensity of the combined waves.
- Use the method of phasors to locate maxima and minima in a two-slit interference problem, multi-slit interference pattern, or for diffraction gratings.
Homework
- Friday's Assigned Problems:
A87, A89, A93, A103; CH 14: 32; CH 32: 11, 13, 41;
Supp CH 1: 5
Answers: CH 14 #32 every 7.5 seconds
- Monday's Hand-In Problems from Lecture 11:
A88, A104; Supp CH 1: 4, 6;
CH 32: 40
Note: this is only the second half of the hand-in set.
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 1; CT2 - 3; CT3 - 6; CT4 - 4
- Excel sheet showing the addition of two waves.
- Online demo of 2-source interference.
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.Pre-Class Entertainment
- The Way You Do The Things You Do - The Temptations
- All Along the Watchtower - Jimi Hendrix
- Piece of My Heart - Janis Joplin
- Domino - Van Morrison
- Superstition - Stevie Wonder
Assigned Problems Guide
- A87: medium. Figure out the path length difference from the description, find the phase difference, and then sketch the phasor diagram and do vector addition.
- A89: medium. Two-source interference. The geometry part of this problem is directly from the diagram. For part (b) you need to know that the intensity is proportional to the amplitude squared.
- A93: medium long. Reading off the amplitudes should be quick. Need to think carefully about the phase difference between the two phasors and do the vector addition.
- A103: medium. Very similar to A93, except the phasor diagram should result in a quicker calculation.
- 14-32: quick. Use the expression for the beating frequency from Lecture 10.
- 32-11: medium long. First, I would reword the question: find the distance between the central maximum and the first side maximum. Then you focus on finding the angle $\theta$ associated with the first side maximum (you know $\theta = 0$ for the central maximum.) Start with knowing the phase difference associated with being a first side maximum and go from there.
- 32-13: Like 32-11, I would focus on the first side maximum, which the problem is telling you is at an angle of $\theta = 0.065^\circ$. Use the given information to get $\Delta r$, and then from that find $\lambda$.
- 32-41: long. You're given $y$, a distance from the center of the screen to the point $P$. Use that and $L$ to find the angle $\theta$, and then proceed to $\Delta r$, to $\Delta\phi$, etc.
- Supp 1-5: medium long. Use the given geometry to figure out $\Delta r$. Then go from there to $\Delta\phi$ and the phasor diagram. Pay attention to the amplitudes!