Here are the given from the question.
Core refractive index (n1) = 1.50
Cladding refractive index (n2) = 1.47
Critical angle at the core–cladding interface φc = ?
Numerical aperture (NA for the fiber) = ?
Acceptance angle in air for the fiber (θa) = ?
(a) To find the critical angle φc from the core and cladding refractive index,
φc = sin−1(n2/n1) = sin−1(1.47/1.5) = 78.5°
(b) The NA can be found by using the equation, NA = (n12 - n22)0.5
= (1.52 - 1.472)0.5
= (2.25 − 2.16)0.5 = 0.3
(c) The acceptance angle in air θa
= θa = sin−1(NA) = sin−1(0.30)