Question

if core refractive index of 1.55 and that of cladding is 1.0.calculate numerical aperture and acceptance angle.​

Answer 1

it has given that, core refractive index is 1.55 and that of cladding is 1.0.

we have to find the numerical aperture and acceptance.

solution : Numerical aperture is a dimensionless quantity that characterizes the range of angles over the system can emit or accept of light. in short, it is a measure how much light can be collected by an optical fibre system.

it is determined by the relative magnitude of refractive index in the core and in the cladding.

formula of numerical aperture is given by, NA = √(n₁² - n₂²) , where n₁ is refractive index in the core and n₂ refractive index in the cladding.

here n₁ = 1.55 and n₂ = 1

so, NA = √(1.55² - 1²) = 1.184

now acceptance angle is the maximum angle of a ray hitting the fiber core which allows the incident light to be guided by the core. it is given by, θ = sin¯¹[NA] = sin¯¹[1.184] = undefined. something is wrong in question. I think refractive index in the cladding is wrong. plz check once again otherwise concept is correct.

maybe your questions is to find acceptance angle in water whose refractive index is 1.33

so, θ = sin¯¹[NA/μ] = sin¯¹[1.184/1.33] ≈ 62.9°