Answer to Question #312035 in Optics for Motasam

Question

Define the relative refractive index difference for an optical fiber and show how it

May be related to the numerical aperture. A step index fiber with a large core diameter compared with the wavelength of the transmitted light has an acceptance angle in air of 22° and a relative refractive index difference of 3%. Estimate the numerical aperture and the critical angle at the core–cladding interface for the fiber.

Answer 1

$\Delta =1-\frac{n_2}{n_1},$

$n_2=0.97n_1,$

$n_2=1,$

$n_1=1.03,$

$NA=\sqrt{n_1^2-n_2^2}=0.25,$

$\beta=\arcsin\frac {n_1}{\sin\alpha}=25°.$