13 Jul 2026

Numerical Aperture of a Step-Index Optical Fibre

practical ug-viii optical-fibre numerical-aperture

Aim

To determine the numerical aperture and acceptance angle of a step-index optical fibre.

Apparatus

Laser diode, step-index fibre, screen, metre scale, fibre holder, and power supply.

Figure

The laser launches light into the fibre; the output cone on the screen gives the spot radius used to calculate numerical aperture.

Theory

The core has refractive index $n_1$ greater than the cladding index $n_2$. Rays entering within the acceptance cone undergo total internal reflection. If the output cone has radius $r$ at distance $L$,

\[\theta_a=\tan^{-1}(r/L),\qquad NA=\sin\theta_a.\]

Observations

$L$ (cm)	Cone diameter (cm)	$\theta_a$	$NA$
20	6.2	$8.8^\circ$	0.153
30	9.4	$8.9^\circ$	0.155
40	12.5	$8.9^\circ$	0.155

Result

\[\boxed{NA=0.154},\qquad \boxed{\theta_a\approx8.9^\circ}.\]

Viva Questions

1. Why does the fibre guide light? By total internal reflection at the core-cladding boundary.
2. What does NA measure? The light-gathering ability of the fibre.
3. Why is the output cone measured? Its geometry gives the acceptance angle.

Maxima Code

Download the Maxima calculation file.