Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link

Light from free space is incident at an angle $${\theta _1}$$ to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are $${n_1}\,\, = \,\,1.5$$ and $${n_2}\,\, = \,\,1.4$$ respectively.

The maximum value of $${\theta _1}$$ (in degrees) for which the incident light will be guided in the core of the fibre is ________ .