Measuring Muka with an Air Wedge

To measure the diameter $D$ of a single fibre of muka (prepared harakeke fibre), a student lays two flat glass microscope slides on top of each other, touching along one edge. The fibre is placed between them, parallel to the line of contact and a distance $L = 75.0\ \text{mm}$ from it, so that a thin wedge of air forms between the slides. The wedge is lit from above at normal incidence with sodium light of wavelength $\lambda = 589\ \text{nm}$ and viewed from above through a travelling microscope; straight bright and dark fringes are seen parallel to the line of contact. Refractive indices: glass $1.52$, water $1.33$.