Question

An air wedge is formed between two glass plates separated at one edge by a very fine wire of circular cross section as shown in Figure. When the wedge is illuminated from above by 600-nm light and viewed from above, 30 dark fringes are observed. Calculate the diameter d of the wire.

Answer 1

For destructive interference in the air,

$2t=m\lambda$

The first dark fringe occurs at the end where the plates meet, where destructive interference occurs because of the phase reversal caused by light reflecting from the top of the lower glass slide. For 30 dark fringes, including the one where the plates meet, m = 29 and

$t=\frac{n\lambda }{2}=\frac{29\left(600nm\right)}{2}$

$=8.70\times {10}^{-6}m=8.70\mu$ m

The diameter of the wire is the same as the thickness :

$d=t=8.70\mu$ m