Answer
114 nm.
Work Step by Step
See figure 35.11. Both rays undergo a $180^{\circ}$ phase change on reflection. There is no net phase difference introduced and the condition for destructive interference is $2t=(m+\frac{1}{2})\lambda$.
For the thinnest film, m=0.
$$t=\frac{\lambda}{4} $$
Note that $\lambda=\frac{\lambda_0}{1.42}$.
$$t=\frac{\lambda_0}{4(1.42)}=\frac{650nm}{4(1.42)}=114 nm $$
