Answer
a) the center of the pattern is a dark spot
b) $r=12.4mm$
Work Step by Step
(a) We know that the light reflected from the lower surface of the lens has no phase change, while the light reflected from the top surface of the flat glass piece undergoes a half wavelength phase change. Thus, they are half a wavelength out of phase, resulting in destructive interference and the center of the pattern is a dark spot.
(b) We can find the required radius as follows:
$r=\sqrt{10\lambda R}$
We plug in the known values to obtain:
$r=\sqrt{10(589\times 10^{-9}m)(26.1m)}$
$r=12.4\times 10^{-3}m=12.4mm$
