Answer
a. 96.4 nm.
b. The next three thicknesses are 192 nm, 289 nm, and 386 nm.
Work Step by Step
See figure 35.11. 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 $\lambda=\frac{\lambda_0}{2.62}$.
$$t=\frac{\lambda_0}{2(2.62)}=\frac{505nm}{2(2.62)}=96.4 nm $$
b. The next three thicknesses are for m=2, 3 and 4: 192 nm, 289 nm, and 386 nm.
