Newton's rings at an oblique angle of incidence of light

[jokPAN]

TL;DR

Why do we get elliptical rings when the light rays fall obliquely?

Good day! Sorry for my bad level of English, but I got a question about the interference of light in the case of Newton's rings.
We know that If light rays fall on an installation consisting of a lens and a reflecting plate perpendicular to the surface of the lens, the interference pattern looks like concentric circles. But why do we get elliptical rings when the light rays fall obliquely? Cannot find anything about it on the net, so please help me figure this out.

 

[sophiecentaur]

Hi. The reason for this is just the geometry of the situation. Interference maxes and mins are due to the difference in path lengths along any direction from the two surfaces involved. So, with one spherical surface and a one plane surface and a normal incidence of light, each curve of minima (say) on the patterns will follow a circle around the central point of contact.
If you consider a simpler system with two plane surfaces, tilted at a small angle, the lines of mimina will be straight and parallel to the line of contact. (Lines of constant path length difference.)
For a spherical surface, illuminated obliquely, the path differences will change quickest with distance for paths in the direction of the illumination (producing narrower fringes) and slower with distance in directions across the direction of illumination (producing wider fringes). This could be looked on as a combination of the two cases above so you would expect 'oval' fringes with spacing dependent on the angle.
Is that enough? Or do you want a formal derivation of actual elliptical fringes? If you want to go further then you may need to do your own calculations. What sort of search criteria have you tried for your query?