An optical fibre has a glass core of refractive index $1.50$, surrounded by a cladding of refractive index $1.40$, as shown in the figure. Light enters the flat end of the fibre from air. What is the largest angle with the fibre's axis at which a ray can enter and still be trapped inside the core by total internal reflection?

Fig. 1: An optical fibre: a core of refractive index 1.50 with cladding of 1.40, and a ray entering the end from air at an angle theta to the axis, reflecting along the core.