Interference of 2 particular waves in Newton's rings experiment The rings formed in this experiment are due to the interference of light reflected from the top and bottom surfaces of the thin film of air between the plano convex lens and the glass plate below it.
My question is, what happens to the light ray that is reflected from the top surface of the plano convex lens and the bottom surface of the glass plate? 
All I could figure was that the red ray undergoes a $\pi$ shift and there is a path difference $2(\mu\cdot t_1+t_2+\mu\cdot t_3)$, where $t_1\, ,t_2$ and $t_3$ are the thicknesses of the lens , the air film and the glass plate respectively.
Is the interference of these waves even a part of the final pattern?
 A: If the source was a laser you may well see fringes due to the interference of waves reflected off the top of the lens and the bottom of the glass plate however it is unlikely that observable fringes are seen if you use a conventional light source.  
The important factor is the size of the optical path difference between the top of the lens and the bottom of the glass plate.  
The path difference between the bottom of the lens and the top of the glass plate is of the order of a few (tens of) wavelengths of light whereas that from the top of the lens and the bottom of the glass plate is many tens (hundreds of) thousands wavelengths of light.  
The coherence length of light from a conventional light source even it is called monochromatic (eg sodium) is much less than the optical path difference between the top of the lens and the bottom of the glass plate and so although the waves overlap they do not form a visible interference pattern.
Other contributory factors are that monochromatic light from a conventional light source is composed of a band of wavelengths and in the case of light from a Sodium source consists of two wavelengths of roughly equal intensity about $0.6 \,\rm nm$ apart.
All these preclude to observation of an interference pattern when there is a large optical path difference between the overlapping waves.
A: I'm not entirely in agreement with the answer above because we do see the coloured rings in a puddle of water if there's a bit of oil in it.  But Farcher could be correct for the lens and glass setup as the oil layers may provide much thinner layers than the setup.
You are correct the answer is interference and if you want to dig a little deeper you might ask what happens to the energy, do the photons really cancel out?  Where does the energy go?  To answer that you have to dig into photon wave functions ....
