At the lower surface, the ray reflects going from air towards glass – low n to high – so the phase change is π. (See Reflections and phases for an introduction.) At the upper surface, the ray reflects going from glass towards air – high n to low n – so the phase change is zero, as indicated on the sketch. Now consider the phase difference due to reflections. The component of phase difference between these two that is due to their different pathlength, which is much less than π. Now consider the reflection from the top surface and that from the bottom: the two parallel rays travelling upwards. Real materials are not infinitely rigid and so they deform at contact and may even weld together.Ĭonsider first the arrows closest to the point of contact, where the separation t between interfaces is rather less than a quarter wavelength, λ/4. * Only in the macroscopic view is there a point of contact. The other surfaces (the top surface of the lens and the bottom surface of the flat) are assumed to be so far away that reflections from them don't produce interference fringes: see Coherence length. This sketch shows the geometry close to the point* of contact between the convext lens (top) and glass flat (bottom). Reflections and phase changes at the glass-air interfaces Reflections and the conditions for constructive and destructive interference This is surrounded by bright and dark circles, due to constructive and destructive interference respectively. In this area, the thin film of air between the lens and the flat has a thickness much less than the wavelength of light. The large dark patch at the centre is around the point where the convex lens surface touches the glass flat below it. We analyse this geometry below.Īt right we see a photograph of the interference pattern. The convex side of the lens has a radius of curvature R and we consider one of the rigns with radius r where the air film between lens and flat has thickness t. The sketch at left shows the global geometry. Left: the global geometry of this Newton's rings setup The geometry and the interference patternĪbove: Newton's rings seen in sodium light
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