The discovery of the device goes back to 1665 and is attributed to Robert Hooke (1635-1703) who in his Micrographia describes the coloured rings produced around the point of contact in the thin layer of air between two lenses with large radii of curvature placed one on the other.
He limited himself to describing the rings without measuring them but, although his attempt at explaining them was based on a completely erroneous principle, he guessed that they were caused by the beams reflected by the two surfaces of the layer of air.
If we take into account the phase shift of p at the reflection between air and glass, it is seen that the clear rings have a thickness the double of which is equal to an odd number of half wavelengths and the dark rings have a thickness the double of which is equal to an even number of half wavelengths, with the consequence that for the former the thicknesses are proportional to the odd numbers and for the latter to the even numbers.
The exact relationship between the radius of the rings, the thickness of the layer of air and the radius of curvature of the lens can be determined geometrically and, neglecting the square of the thickness with respect to the square of the radius of curvature of the lens, from that relationship it can be calculated that the radius of the generic ring is equal to twice the product of the thickness of the layer of air multiplied by the radius of curvature of the lens. ...continues