Newton's Rings -- from Eric Weisstein's World of Physics

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Newton's Rings

Given a hemisphere Eric Weisstein's World of Math of radius Eric Weisstein's World of Math R resting on a plane, monochromatic light falling normally on the top of the hemisphere reflects off both the plane and the hemisphere. Eric Weisstein's World of Math Near the center of the hemisphere, refraction can be neglected, and the rays create rings of interference. On the curved surface, a point a distance r from the center will be a height d above the plane

(1)

(2)

Reflection from hemisphere undergoes a phase change of . Reflection from the plane gives a phase change of . The phase difference between rays reflected off the plane and hemisphere is therefore

(3)

for , and the interference pattern goes as .


© 1996-2007 Eric W. Weisstein

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