Question $10,$ chap $137,$ sect $7.$

part $1$ of $\backslash (1\backslash$quad $10\backslash )$ points

An air wedge is formed between two glass plates separated at one edge by a very fine wire as shown.

When the wedge is illuminated from above by $600$ nm light, $45$ dark fringes are observed. The count here includes the dark fringe at the contact point.

Calculate the radius of the wire. Answer in units of $\backslash (\backslash$mu $\backslash$mathrm$\{$m$\}\backslash ).$