8. In an acute triangle $\triangle A B C$, the lengths of the sides opposite to $\angle A, \angle B, \angle C$ are $a, b, c$ respectively. If
$$
\frac{b^{2}}{a c} \geqslant \frac{\cos ^{2} B}{\cos A \cdot \cos C},
$$

then the range of $\angle B$ is $\qquad$ .
8. $\left[\frac{\pi}{3}, \frac{\pi}{2}\right)$.

By the cosine rule, we have
$$
\frac{b^{2}}{a c} \geqslant \frac{\left(\frac{a^{2}+c^{2}-b^{2}}{2 a c}\right)^{2}}{\frac{b^{2}+c^{2}-a^{2}}{2 b c} \cdot \frac{a^{2}+b^{2}-c^{2}}{2 a b}} \text {. }
$$

Simplifying it, we get
$$
b^{2} \geqslant \frac{a^{4}+c^{4}}{a^{2}+c^{2}}=a^{2}+c^{2}-\frac{2 a^{2} c^{2}}{a^{2}+c^{2}} \text {. }
$$

Then $\cos B=\frac{a^{2}+c^{2}-b^{2}}{2 a c} \leqslant \frac{a c}{a^{2}+c^{2}} \leqslant \frac{1}{2}$.