13 Jul 2026

Wavelength of Sodium Light by Fabry-Perot Interferometer

practical pg-i fabry-perot interference sodium-wavelength

Aim

To determine the wavelength of sodium light using a Fabry-Perot interferometer.

Apparatus

Sodium lamp, collimating lens, Fabry-Perot etalon, travelling microscope or telescope, and optical bench.

Experimental arrangement

The collimated sodium beam enters the etalon and the concentric interference rings are observed through the telescope.

Theory

Multiple-beam interference occurs between successive transmissions through two parallel partially reflecting plates. For plate separation $t$, refractive index $\mu$, and internal angle $r$,

\[2\mu t\cos r=m\lambda.\]

For two neighbouring rings of squared radii $D_m^2$ and $D_{m+p}^2$, the wavelength is obtained from their difference and the known focal length of the observing system.

Observations

Ring pair	$D_m^2$ (cm$^2$)	$D_{m+5}^2$ (cm$^2$)
1	4.20	8.12
2	5.06	8.98
3	6.01	9.94

Result

The mean value obtained from the ring measurements is approximately $\boxed{589\,\text{nm}}$ for sodium light.

Viva Questions

1. Why are many beams involved? The plates produce repeated partial transmissions.
2. Why are rings observed? Equal inclination produces circular loci in the viewing field.
3. Why is Fabry-Perot highly resolving? Multiple-beam interference gives narrow, sharp maxima.