Question

A step index fibre has a relative index difference of 0.9%. Estimate the critical angle at the core-cladding interface, when the core index is 1.46 find the numerical aperture, if the source to fibre medium is air.

Answer 1

Here, ${\mu }_1=1.46;$
$\frac{{\mu }_1-{\mu }_2}{{\mu }_1}=\frac{0.9}{100}=0.009or1-\frac{{\mu }_2}{{\mu }_1}=0.009$
$or\frac{{\mu }_2}{{\mu }_1}=1-0.009=0.991$
Critical angle,
${\theta }_c={\sin }^{-1}\frac{{\mu }_2}{{\mu }_1}={\sin }^{-1}0.991={82.3}^0$
${\mu }_2=0.991\times {\mu }_1=0.991\times 1.46=1.45$
$NA=\sqrt{{{\mu }_1}^2-{{\mu }_2}^2}=\sqrt{{\left(1.46\right)}^2-{\left(1.45\right)}^2}=0.17$