Recap - Optical Fiber

An optical fibre has a glass core (n₁ = 1.5) inside a cladding (n₂ = 1.4). Light that hits the core's side past the critical angle bounces along it. Light enters the end of the fibre from air at an angle α to the fibre's axis, and bends to an angle β to the axis inside the core; the side is parallel to the axis, so the light meets the side at 90° − β from its normal. What is the largest angle α for which the light stays inside the core?