The two angles
Snell's law gives the critical angle at the core wall, measured from the perpendicular: sin(critical angle) = n2 / n1. Light striking the wall at a larger angle than that is totally reflected.
Working back to the fiber's end face gives the numerical aperture, NA = square root of (n1 squared minus n2 squared). The largest entry angle from air that will still be trapped is asin(NA). The zigzag path in the scene is a ray picture; very thin single mode fibers really carry light as a wave pattern.
Why the index step is small
Telecom fibers use a tiny index difference, often under 1 percent, because rays at very different angles travel different distances and spread a pulse out in time. A small step keeps pulses sharp, which allows faster data rates.