let's consider a Fabry-Perot interferometer:
Illumination is provided by a diffuse source, and its rays are focused towards the cavity by a lens. Inside the cavity there are multiple reflections and transmissions of rays. Rays transmitted towards right will have a certain phase shift depending on the input wavelegth. Therefore, we may see only certain wavelegth on a screen at right, because the cavity acts like a filter because the output rays intensity is expressed by the Airy function, which has very strict peaks:
So, the wavelengths that correspond to those peaks are seen on the screen (rays interfere constructively), others are not seen (rays interfere destructively).
Now my question is: why do why see the circles in the first picture on the screen? It seems to me that the lens at right focuses all the transmitted rays in the same point A'. So I'd say that at A' we will see "light" from certain wavelength, "dark" from others. No other points of the screen receive rays, in that picture.