All Problems Interference of Light
Problem 5.95
When a Fabry-Perot étalon is illuminated by monochromatic light with wavelength \(\lambda\) an interference pattern, the system of concentric rings, appears in the focal plane of a lens (Fig. 5.18). The thickness of the étalon is equal to d. Determine how (a) the position of rings; (b) the angular width of fringes depends on the order of interference.
5.95. (a) The condition for maxima: \(2 d \cos \theta=k \lambda\); hence, the order of interference \(k\) diminishes as the angle \(\theta,\) i.e. the radius of the rings, increases (see Fig. 5.18 ). (b) Differenting both sides of the foregoing equation and taking into account that on transition from one maximum to another the value of \(k\) changes by unity, we obtain \(\delta \theta=1 / 2 \lambda / d \sin \theta ;\) this shows that the angular width of the fringes decreases with an increase of the angle \(\theta,\) i.e. with a decrease in the order of interference.