Answer
a). $158.2nm$
b). $316.4nm$
Work Step by Step
a). The condition of constructive interference :-
$\Delta L=2t=\frac{mv}{2n_{1}}$, m=1,3,5........
$t=\frac{mv}{4n_{1}}$, m=1,3,5.......
in air, $t=\frac{v}{4n_{1}}=\frac{632.8\times 10^{-9}}{4\times1}=158.2nm$
b). The second reflected beam is $180^{\circ}$ phase shift so the condition of destructive interference :-
$\Delta L=2t=\frac{mv}{n_{1}}$, m=1,2,3........
$t=\frac{mv}{2n_{1}}$, m=1 for minimum thickness
$t=\frac{632.8\times10^{-9}}{2\times1}=316.4nm$
