Monochromatic light from a step index $(n_1=1.500;n_2=1.485),$ multimode optical fiber of core diameter $100\;\mu m$ is incident through air $(n=1.000)$ onto a linear photo-detector array placed at $1\; mm$ distance from the tip of the fiber. The tip of the fiber is polished and its exit plane is perpendicular to the axis of the fiber. the detector array is oriented parallel to the exit plane of the tip. The array consists of photo-detector elements each of $5\;\mu m $ diameter. The distance between the edges of two adjacent elements can be assumed to be zero. The number of elements illuminated by the light coming out of the fiber is __________.