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Newton’s rings are formed as a result of interference between light waves reflected from the upper and lower surfaces of the air film developed between the convex surface of the plano-convex lens and plane glass plate.

this is what I have seen in most textbooks and websites

reflection from curved surface and flat surface

Then What happens to the light reflected from the upper surface of the lens and the lower surface of glass plate?

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The reflected light you refer to will not give you interference fringes, because the path difference between the two routes (via top of lens and via another surface) is too big. If the path difference is greater than a few wavelengths (perhaps about 50* but see Farcher's comments below) – more if you are using laser light) the wavelength-spread of the light will mean that some wavelengths will interfere constructively and others destructively (and everything in between), so the reflected light that you refer to will just contribute to a brighter background, without giving its own fringes (that is rings).

On the other hand, light reflected from the top surface of the flat glass and from the bottom surface of the lens will produce fringes, because near the centre (the point of contact) the path difference is so small. For example, if the radius of curvature of the bottom surface of the lens is 1.0 m, then at 5 mm from the centre, $\Delta y = 125 \times 10^{-7} \text{m},\ $ which is probably about 20 wavelengths. Note that further out, even these fringes start to blur out, for the reason given in my first paragraph.

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  • $\begingroup$ You are correct about the path difference being too large but have underestimated the path difference at which fringes will be seen with a conventional light source. With a Sodium source the fringes disappear at an order of approximately 490 and reappear at order 980 which corresponds to a path difference of approximately half a millimetre. The modulation in intensity is due to there being two relatively narrow Sodium lines separated by a wavelength of about 0.6 nm. arxiv.org/pdf/1304.7586.pdf $\endgroup$
    – Farcher
    Commented Jul 31, 2018 at 14:41
  • $\begingroup$ I was thinking of a white light source with a coloured gel filter, but I suppose that is really archaic! $\endgroup$
    – Philip Wood
    Commented Jul 31, 2018 at 15:06
  • $\begingroup$ Not archaic at all and if you see twenty fringes you are doing well! $\endgroup$
    – Farcher
    Commented Jul 31, 2018 at 15:09

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