# The numerical aperture of optic fibre and angle of incidence

First
My college book contains the following passage:

the angle of incidence (relative to the fibre axis ) can't be too large else the ray would be refracting on the core\cladding boundary and transmitted outside the fiber and a very small percentage passes.

Here's how I reasoned and I'd like to be corrected. The geometry I imagined was as follows:

• light falls with a very large angle $\alpha$ from air,
• light is refracted with angle $\theta$, $\theta$ < $\alpha$,
• light falls on cladding with large angle $\beta$ where: $\alpha > \beta$ and $\beta > \theta c$ of the material of the cladding,
• light is simply totally internally reflected.

Second

I looked it up and found numerical aperture and acceptance angle articles but I'd like to be cleared out on the first matter first.