Question

A silica-glass fiber has a core refractive index of 1.47 and a cladding refractive index of 1.44. If the cladding is completely stripped out and the core is dipped in water of refractive index 1.33, the numerical aperture (rounded to three decimal places) is ____

Hint:

If cladding is stripped, treat the surrounding medium as the new “cladding” when computing NA.

Answer 1

Correct Answer: 0.62

For a step-index fiber surrounded by a medium of refractive index \(n_s\), the NA is \[ \mathrm{NA}=\sqrt{n_1^2-n_s^2}, \] where \(n_1\) is the core index and \(n_s\) is the surrounding medium’s index (here water, since cladding is removed). Thus \[ \mathrm{NA}=\sqrt{1.47^2-1.33^2} =\sqrt{2.1609-1.7689} =\sqrt{0.3920} =0.626 \;. \] Final Answer: 0.626