The refractive indices of core and cladding materials of a step index fibre are 1.48 and 1.45 respectively. Calculate (1) Numerical Aperture, (2) acceptance angle, (3) the critical angle at the core cladding interface, (4) fractional refractive indic…

Given: \(n_1=1.48\), \(n_2=1.45\), \(n_0=1\) (air).

(1) Numerical aperture:

\[ NA=\sqrt{n_1^2-n_2^2}=\sqrt{2.1904-2.1025}=\sqrt{0.0879}=0.2965 \]

(2) Acceptance angle: \(\theta_a=\sin^{-1}(0.2965)=17.25^\circ\)

(3) Critical angle: \(\theta_c=\sin^{-1}\dfrac{n_2}{n_1}=\sin^{-1}(0.9797)=78.44^\circ\)

(4) Fractional index change: \(\Delta=\dfrac{n_1-n_2}{n_1}=\dfrac{0.03}{1.48}=0.0203\) (≈ 2.03%)

NA ≈ 0.297; \(\theta_a\approx17.25^\circ\); \(\theta_c\approx78.44^\circ\); \(\Delta\approx0.0203\)

Check: \(n_1\sqrt{2\Delta}=1.48\sqrt{0.0405}=0.298\approx NA\). The values are consistent.