1. Let the right vertex of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$ be $A$, the upper vertex be $B$, and the left focus be $F$. If $\angle A B F=90^{\circ}$, then the eccentricity of the ellipse is $\qquad$.
$$
b^{2}=a c \Rightarrow a^{2}-c^{2}=a c \Rightarrow e^{2}+e-1=0 \Rightarrow e=\frac{\sqrt{5}-1}{2}
$$

The translation is as follows:
$$
b^{2}=a c \Rightarrow a^{2}-c^{2}=a c \Rightarrow e^{2}+e-1=0 \Rightarrow e=\frac{\sqrt{5}-1}{2}
$$