Worked example - numerical aperture of a typical fibre. Core n1 = 1.48, cladding n2 = 1.46. Step 1: NA = sqrt(n1^2 - n2^2) = sqrt(2.1904 - 2.1316) = sqrt(0.0588) = 0.2425. Step 2: acceptance angle theta_a = arcsin(NA) = arcsin(0.2425) = 14.0 degrees - light entering within this half-angle cone is trapped. Step 3: critical angle at the core-cladding wall: theta_c = arcsin(n2/n1) = arcsin(1.46/1.48) = arcsin(0.9865) = 80.6 degrees from the normal (i.e. just 9.4 degrees from grazing). Rays steeper than this leak out - which is why bending a fibre too tightly spills light.