Modified: March 9, 2023
[Solved] A silica optical fiber with a core diameter large enough to be considered by ray theory analysis has a core ...
Question:
A silica optical fiber with a core diameter large enough to be considered by ray theory analysis has a core refractive index of 1.50 and a cladding refractive index of 1.47.
Determine: (a) the critical angle at the core–cladding interface; (b) the NA for the fiber; (c) the acceptance angle in air for the fiber.
Solution/Given:
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)
= 17.4°
