Answer to Question #87665 in Optics for Shivam Nishad

Question #87665
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.
1
Expert's answer
2019-04-15T10:13:10-0400

The numerical aperture:


NA=ncore2ncladding2=0.42.NA=\sqrt{n_{core}^2-n_{cladding}^2}=0.42.

The acceptance angle can be determined from the numerical aperture:


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

α=sin1NAnmedium=sin10.421=24.83.\alpha=\text{sin}^{-1}\frac{NA}{n_{medium}}=\text{sin}^{-1}\frac{0.42}{1}=24.83^\circ.

The critical angle:


ncladdingsin90=ncoresinαcritical,n_{cladding}\text{sin}90^\circ=n_{core}\text{sin}\alpha_{critical},

αcritical=sin1ncladdingncore=73.90.\alpha_{critical}=\text{sin}^{-1}\frac{n_{cladding}}{n_{core}}=73.90^\circ.


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