= Newton's rings
{c}
= Newton rings
{synonym}
A curved transparent surface resting on a plane traps a thin film whose thickness increases radially, producing circular <interference fringes>. For near-normal reflected <light> and one relative $\pi$ reflection <wave phase> change, contact is dark and bright rings obey $2nt=(m+1/2)\lambda_0$ for $m=0,1,\ldots$. Here $n$ is the film's <refractive index> and $\lambda_0$ the vacuum <wavelength>. For spherical curvature radius $R$, $t\simeq r^2/(2R)$ gives $r_m^2=R\lambda_0(m+1/2)/n$. Consequently $D_{m+s}^2-D_m^2=4sR\lambda_0/n$ for ring diameters $D_m=2r_m$. A contact gap, altered reflection phase, or significant oblique incidence changes the formula.
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