A silica step-index fibre has core refractive index 1.48 and cladding refractive index 1.46. The fibre end is first kept in air and later completely immersed in water of refractive index 1.33.
(a) Derive a general expression for the largest external incident angle θ0 in terms of the outside medium’s refractive index n0, n1, and n2.
(b) Using this result, calculate θ0 (to one decimal place) when (i) the fibre end is in air and (ii) it is immersed in water.
(c) Determine the percentage decrease in the light-collecting ability of the fibre on immersion, assuming it is proportional to sin2θ0.