# Newton rings: spherical droplet with thin film interference

## Homework Statement

So I have a similar situation with the traditional newton rings. Instead of having however a convex lens, I have a (partial) spherical surface with height d with sitting on top of a thin film of thickness t, with d >>> t, and refractive index n and below the thin film is a mirror. I have to find what is the condition for constructive/destructive interference for the resulting newton rings.

## The Attempt at a Solution

I know that: i have optical length inside the spherical surface of the would be $$d$$, so the optical path would be $$2d$$. Also, I have an optical length inside the thin film, where there would also be a phase change of $$\pi$$. So total change of phase would be $$2d+2t+\pi$$.

Also, from the geometry You can infer that:$$r_m^2 = t*(2R-t)$$ where $$r_m$$ would be the radius of the mth dark ring and $$R$$ the radius the circle (curvature of the lense).