When a Fabry-Perot etalon is illuminated by monochrmatic light with wavelength `lambda` an interference pattern, the system of concentric rings, appears in the focal plane of a lens (Fig.) The thickness of the etalom is equal to `d`. Determine how

(a) the position of rings,
(b) the angular width of fringes depends on the order of interference.

Explanation

The path difference between `(1) & (2)` can be seen to be
`Delta = 2d sec theta - 2d tan theta sin theta`
=` 2d cos theta = k lambda`
for maxima. Here `k =` half-interger.
The order of interference decreases as `theta` increases i.e. as the radius of the rings increases.
(b) Differentiating
`2d sin theta del theta = lambda`
on putting `del k =- 1`. Thus
`del theta = (lambda)/(2d sin theta)`
`del theta` decreases as `theta` increases.