The Newton’s rings device yields rings in view of its rotational symmetry. Another difference is highlighted by the type of reflections involved. Reflection is of the glass-air type on the spherical diopter of the lens, and of the air-glass type on the mirror.nNewton’s rings are in this case observed in transmission as the flat plate is transparent. The central ring is thus bright.

We illuminate at normal incidence, with a monochromatic parallel beam of light, a large-radius convex flat lens placed on a glass slide. Part of a ray is reflected on the glass-air interface  without phase change, while the other part passes through this  interface, and a fraction of this ray is reflected on the bottom slide.  As this ray is reflected by a more refractive medium, this reflection  produces a phase shift of π. These two reflected rays, of adjacent  amplitudes, interfere by yielding localised fringes (as for thin plate)  in the vicinity of the lens spherical surface. Let R be the radius of  curvature on the underside of the lens. In other words r = OI is

the  distance between the ray and the optical axis of the system. As r is far smaller than R, we obtain: e ≈ r2 / 2R. The optical path  difference is formulated as δ = 2e + λ / 2 = r² / R + λ / 2. As the  system accepts an axis of revolution, fringes are rings centred on this  axis. Dark rings are obtained when δ = (2k +1) λ / 2 or for 2e = r2 / R =  kλ. If the lens is in optical contact with the underside, the first  ring will be dark. The following rings (the optical path difference  increases by one wavelength between two rings) have radii proportional  to the square root of an integer.