Answer
$1.0~cm$
Work Step by Step
We know that the length of the bands on the glass plate is given as
$a=\frac{0.052\times 10^{-3}m}{2.857\times 10^{-5}m}$
$a=1.82m$
Now, the number of dark bands formed is given as
$m=\frac{2d}{\lambda}$
$m=\frac{2(0.052\times 10^{-3}m)}{589\times 10^{-9}m}$
$m=177 dark \space bands$
Now, the distance between the adjacent dark bands can be determined as
$t=\frac{1.82m}{177}$
$t=0.0103075m=1.03075cm$
