14. As shown in the figure, the axial section of the reflector on the spotlight bulb of a movie projector is part of an ellipse, with the filament located at focus $F_{2}$, and the distance between the filament and the vertex $A$ of the reflector $|F_{2} A|=1.5$ cm, and the latus rectum of the ellipse $|B C|=5.4$ cm. To ensure the film gate of the movie projector receives the strongest light, how far from the film gate should the bulb be placed?
14. According to the optical properties of the elliptical mirror, light rays emitted from one focus of the ellipse are reflected and converge at the other focus. Therefore, the lamp should be placed at focus $F_{1}$ to obtain the strongest light. For this, the focal distance needs to be determined.

Assume the equation of the ellipse is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, then $B(c, 2.7)$, and $a-c=1.5$. From $\frac{c^{2}}{a^{2}}+\frac{2.7^{2}}{b^{2}}=1, a-c=1.5, a^{2}=b^{2}+c^{2}$, we solve to get $a=7.5, b=4.5, c=6$. That is, the lamp should be installed 12 centimeters away from the film door.