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# Problem Set of Interference and Parallel Plates

2.7 Suppose a virtual image is located 8 cm to the right of a lens which has a focal length of -12 cm. Find the location of the object. (Answer: 24 cm to the right.)

3.8 Suppose two parallel plates of glass are separated uniformly by a very small distance. Show that constructive interference occurs when the thickness and wavelength are related by
2t = (m + 1/2)(lambda)
Here, t is the thickness of the air gap and m is an integer, 0, 1, 2, etc. You will provide a diagram and a narrative clearly showing how you obtain this expression. (You don't need to worry about the thickness of the glass plates themselves.)

3.9 In the problem above, how would the expression be modified if there were water or oil between the plates instead of air?

3.10 Imagine a coordinate system with marks 1 meter apart, in the x- and y-directions. A speaker at the origin is producing sound of a single frequency, 660 Hz. There is another speaker on the x-axis, at x = 2.0 m, producing an identical sound. Question 1: at the point (0, 3.56 m), is there constructive interference or destructive interference of the sound from the two speakers? Question 2: What about at the point (0.60 m, 2.85 m)? Hint: find the wavelength, and then find the path length difference from the speakers to the point in question. Assume the speed of sound to be 343 m/s. Drawing a diagram will help.

#### Solution Summary

The solution is attached as a .doc and .pdf file that explains the 4 questions about using speakers and virtual images.

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