A step-index optical fibre has core refractive index and cladding refractive index

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

A step-index optical fibre has core refractive index

n_{1}

and cladding refractive index

n_{2}

(n_{1} > n_{2})

. Light is launched from air into the flat end of the fibre at an angle

\theta_{0}

with respect to the fibre axis. (a) Derive an expression for the maximum value of

\theta_{0}

for which the light will be guided by total internal reflections inside the core. Express your result in terms of

n_{1}

and

n_{2}

. (b) Using your result, calculate (i) the maximum entrance angle and (ii) the numerical aperture for a fibre with

n_{1} = 1.48

and

n_{2} = 1.46