= Angular fringe spacing of a transparent film
For a film of <refractive index> $n$ and thickness $d$ in air, its round-trip propagation <phase> is $\delta=(4\pi d/\lambda_0)\sqrt{n^2-\sin^2\theta_i}$. Two neighbouring same-type <interference fringes> differ by $2\pi$. At small angular spacing in radians,
$$
\Delta\theta_i\simeq\frac{\lambda_0\sqrt{n^2-\sin^2\theta_i}}{2d\sin\theta_i\cos\theta_i}
=\frac{\lambda_0 n\cos\theta}{2d\sin\theta_i\cos\theta_i}.
$$
The relation assumes slowly varying interface <reflection coefficients> and no rapidly varying reflection phase. At normal incidence the first derivative vanishes, so a local linear angular-spacing formula must be replaced by a quadratic expansion.
Back to article page
