Answer
180 nm.
Work Step by Step
See figure 35.11. Consider light reflected at the front and rear surfaces of the film. One ray undergoes a $180^{\circ}$ phase change on reflection. There is a net phase difference introduced, and the condition for destructive interference is $2t=m \lambda$.
For the thinnest film, m=1.
$$t=\frac{ (1) \lambda}{2} $$
Note that $\lambda=\frac{\lambda_0}{1.33}$.
$$t=\frac{\lambda_0}{2(1.33)}=\frac{480nm}{2(1.33)}=180 nm $$
