2. The cross-section obtained by cutting a cylinder with a plane at an angle of $30^{\circ}$ to the cylinder's axis is an ellipse. The eccentricity of this ellipse is ( ).
(A) $\frac{1}{2}$
(B) $\frac{\sqrt{2}}{2}$
(C) $\frac{\sqrt{3}}{2}$
(D) $\frac{\sqrt{3}}{4}$
2.C.

Let the radius of the cylinder's base be $r$, and the semi-major and semi-minor axes of the ellipse be $a, b$. Then $a=2r, b=r, c=\sqrt{3}r$. Therefore, $e=\frac{c}{a}=\frac{\sqrt{3}}{2}$.