Fabry-Pérot Interferometer: Airy Formula & Resolving Power

UPSC IFoS / CSE Paper I — Physical Optics

1. Principle & Multiple-Beam Interference

The Fabry-Pérot interferometer consists of two high-reflectivity parallel glass plates separated by a fixed distance d.

Let R be the plate reflectance and T = 1 - R the transmittance. The transmitted intensity distribution is described by the famous Airy formula: I_t = \frac{I_0}{1 + F \sin^2(\delta / 2)}

where:

• \delta = \frac{4\pi d}{\lambda} \cos\theta is the phase difference between adjacent beams.
• F = \frac{4R}{(1 - R)^2} is the Coefficient of Finesse.

2. Resolving Power (Chromatic Resolution)

The chromatic resolving power measures the instrument's ability to separate two close wavelengths \lambda and \lambda + \Delta\lambda:

\frac{\lambda}{\Delta\lambda} = m \mathcal{F}

where:

• m = \frac{2d}{\lambda} is the order of interference.
• \mathcal{F} = \frac{\pi \sqrt{R}}{1 - R} is the Reflective Finesse of the cavity.

For R = 0.95, \mathcal{F} \approx 61, providing exceptionally narrow transmitted fringes ideal for studying hyperfine structure and isotopic shifts in atomic spectra.