Solve the following:
Problem Set of Interference and Parallel Plates
Q1: 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.
Q2: 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.
Q3: In the problem above, how would the expression be modified if there were water or oil between the plates instead of air?
Q4: 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.
a: at the point (0, 3.56 m), is there constructive interference or destructive interference of the sound from the two speakers?
b: 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.