A plane wave hits a piece of glass whose front surface is spherical and whose back surface is plane. The radius of the lens is 10 cm and the thickness of the glass is 1 cm at the center, as shown in the diagram at right. At time t1, the center of the plane wavefront has just reached the lens. A short time later, at time t2, the center of the wavefront will have passed completely through the glass, as shown.
a) Find the time that elapses between t1 and t2, the time it takes the center of the wavefront to pass thorugh the middle 1 cm of the glass.
b) Find the amount by which the edges of the wavefront at t2 will be ahead of the cetner of the wavefront, due to the fact that these edges passed through empty space, with no glass in their paths.
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