Question

Calculate the critical angle, numerical aperture and acceptance angle for a silica fibre
in air with core refractive index 1.53 and cladding refractive index 1.47.

Answer 1

The numerical aperture:

$$NA=\sqrt{n_{core}^2-n_{cladding}^2}=0.42.$$

The acceptance angle can be determined from the numerical aperture:

$$NA=n_{medium}\text{sin}\alpha,$$

$$\alpha=\text{sin}^{-1}\frac{NA}{n_{medium}}=\text{sin}^{-1}\frac{0.42}{1}=24.83^\circ.$$

The critical angle:

$$n_{cladding}\text{sin}90^\circ=n_{core}\text{sin}\alpha_{critical},$$

$$\alpha_{critical}=\text{sin}^{-1}\frac{n_{cladding}}{n_{core}}=73.90^\circ.$$